Long response is long... but hopefully it'll give you lots to work on.
I know how you feel. Yes, it's bloody hard. But it
does get better. You're currently in the most difficult part of transition: the part between your acceptance of yourself as being trans, and being able to actually do something about it. As soon as you realise you need to transition, it's only natural to want to start transitioning
yesterday. It feels terrible right now, but that eases dramatically once you start seeing a therapist at a GIC. The stress you're experiencing comes from feeling stuck in a rut with no way of moving forward. Once you're getting treatment, you feel a heck of a lot less stressed about it because you can see the light at the end of the tunnel.
I notice you've only been posting since December: that's only three months' worth of posts. And you've said you're not 100% sure you're trans and you're worried your Mum may think it's just a phase. To be honest, kids go through phases all the time and anyone who's raised a child will be familiar with these phases, so it's only natural that your Mum might think that. But phases tend to last for less than 6 months before you move onto the next big thing. So think about how long you've been feeling this way, and if it's something that's only happened within the last few months, you'll probably know within the next few months whether it's a phase or something more serious. But if it's something you've been struggling with for years, you already have your answer.
Every country has different rules about what you can & can't do; how you can get help; and at what age you can get help. I presume from your posts that you're still quite young; possibly a teenager (if you're under 18, please don't post your age here). And your use of 'Mum' and the timing of your posts would suggest that you're probably in the UK/Ireland. So I'm going to presume you're in the UK and advise you accordingly.
Firstly, make whatever small changes you can to help minimise your dysphoria. It might be difficult to do this if you don't have your own sources of income, but simple changes can help enormously without costing the Earth. E.g. change to a men's deodorant (or a fragrance-free one); stop shaving your legs & pits; change your underwear to men's underwear or even women's boxer-style underwear if you aren't allowed to get the real thing; and if you have any supportive friends, ask them to refer to you using your chosen name & pronouns so you can have some oases of calm where you get to feel normal for a change. And next time you get your hair cut, go to a barber shop rather than a hairdresser's for a proper masculine cut. It's cheaper, and they won't try to 'prettify' it like hairdressers do (no matter what cut you ask for, if a hairdresser thinks you're female they'll always try to do a feminine version of it).
Secondly, if you do have some available income then Silver Centurion's sports bra suggestion is a good one. Always get one with as small a cup size as you can comfortably manage, because they'll help squish the offending bits. Then try layering your clothing: a T-Shirt, followed by a button-up shirt; followed by a hoodie can go a long way towards minimising your profile - especially if you buy them in larger sizes than you need (e.g. if you're a Small, buy a Large).
You can also get binders from various places, even if you don't have a bank account for online purchases: if you have cash, you can use it to buy a pre-paid visa card that you can then use to buy stuff on Amazon, including Underworks binders. And Amazon delivers to shopping centres, railway stations etc. around the country so you wouldn't even need to worry about having it delivered to your home. Or you could have it delivered to a friend's house; or school/college; or whatever. It's just an Amazon package; nobody needs to know what's inside it. It looks like it contains a DVD or something.
On that subject, if you wanted to pack your underwear you could start by using a rolled-up pair of clean socks or underwear (both of which will cost you nothing!) or you can buy packers online from various places, including Amazon - but only if you're 18 or older. A good one to start with is the Mr Limpy Extra-Small, which will set you back around a tenner.
Start changing your wardrobe to men's clothing. There are plenty of retailers who sell stuff that will fit; at the beginning of my transition I did a reconnoissance mission to check out the men's departments of all the major retailers, looking for stuff I liked that fitted. Then I started replacing everything piece-by-piece. My early wardrobe was mostly by Primani, with a few pricier pieces from elsewhere. And you know what? Just knowing that the £2 T-Shirt you're wearing is a men's shirt rather than a women's shirt can make you feel so much better.
If swimming is your goal then buy a rash vest from a sports shop (in the surfing section) & wear that over a sports bra. These are usually permitted in the pool because they're designed for use in water, but it's always a good idea to have a quiet word with the manager first to check that it's OK. If needs be, you can explain why you need to wear the vest or simply that it's due to a Protected Characteristic under the Equality Act. Once you're in the water you can't see what's going on in your chest region anyway, so that's a good way to continue swimming if it's something you love doing. And if permitted, keep your towel at the poolside so you can wrap it around yourself ASAP once you leave the water.
As for where to go to get professional help: if you're under 16 you need your parents' permission to see the GP, and your parents are entitled to know why you're seeing them. But if you're 16 or older you can see your GP without your parents' permission or knowledge. So find your GP's phone number and phone them up asking for an appointment. When you get there, tell them you're trans & that you want a referral to a GIC. The waiting lists are hella long at the moment, but there are several clinics around the country, depending on your age. So do some research first about where you'd prefer to be seen & look at the various waiting lists so you can ask your GP to refer you to the correct one. You have a waiting list of at least a year for a first appointment (in some cases it's much longer) so the sooner you get on the list the better. And yes, GICs are also the right place for people who are not absolutely sure they're trans.
Sadly, it takes the rest of the world a heck of a lot longer to catch up - but this is especially true of our parents. You've mentioned your Mum in other threads: during her pregnancy she probably built up an imaginary picture of who you should be and you should be like... and she's been working under those assumptions for your entire life. That's going to take her a long time to unlearn, but it is possible for our families to come round. It's also possible for them to react badly... and none of us really know how our families will react until we come out to them. So get as much support as you can from your friends, from your school/college/colleagues and from other trans people, because you'll need to turn to that support if your Mum reacts badly. And choose carefully when you want to come out, and what you want to say: if you're not 100% sure, be honest about that. You could simply tell her you're struggling with your gender & you want to speak to an expert about it to help you be sure. And remember: even if she says 'no' now, that doesn't mean you can't try again later.
TL;DR: there's stuff you can do right now - and here are the details.
