You are the only one who can decide if going on T (or transitioning at all) is right for you. Do not let anyone else try to tell you what is "best" for you - not even your family.
Whatever your concerns are about going on T, or about the transition, write them down. Discuss them with the appropriate people (IE your doctor, endocrinologist, therapist, etc.) That's why these people are there. And keep in mind that they would NOT have given you your letter, cleared you, or be prescribing you T if they thought it was going to be dangerous or detrimental to your overall well being.
I knew from day one that my goal was hormones. Once i figured out that i was trans and identified as male (that's a whole other LOOONG story) i knew what i wanted to do. Get on hormones, change my name and gender marker, transition socially, top surgery, etc. It took me a while to get here, but i've been on T for four months (almost - will be four months on the 22nd) and even thought i was freaking out when i went in for my first shot... the past four months have been... there are no words for it.
Unfortunately there is no magic crystal ball that will tell you if you'll be happy on T. But the fact that you came this far, that you have your letter and approval to start, means SOMETHING. While i don't encourage anyone to go into transitioning with the mindset that "i can always stop if i want"... there is some truth to it. If you get your first shot, or even your second or third, and it doesn't feel right to you.... then you CAN stop. For the first month or so, TYPICALLY, any changes you see will likely be reversible. After that, there is no guarantee. Once the voice drops that's it, that won't change back. Even if you're on T for months, years, you can stop - some thing won't change back, and de-transitioning is really hard... but it is do-able.
Like i said, though, discuss your concerns with your doctors. Go from there.
Re: your mom. What exactly is she saying that is making your fearful? Don't let her scare you. Listen to her concerns, acknowledge them, then try to prove her wrong with the facts. She is your parent, she has the right to worry about you, and this is a HUGE thing for not just you but HER as well. It is SCARY for a parent to go through. I think that sometimes some of us forget that our transitioning isn't just about us, but about everyone around us. Has she ever gone to therapy with you? Is that something you/she would be comfortable doing? Have you discussed her with your therapist before?
Both of my parents are scared. I have health issues that they are worried will be made worse by the T. I went to specialists to prove that there was no risk. They're less worried, but still ask me how i'm feeling pretty much every day. They're super nervous about possible surgery (we haven't even talked about it - they're still dealing with me being on T). They're also worried about my social transition - how people will react once i change (neighbors, co-workers, etc) and if i'll have issues in the future. They're my parents, it's their job to worry (as they say). That's why we're going to therapy together.
Re: the shots. Yes, you do get used to it. If you want it bad enough, you'll get into a routine and eventually won't even notice it. How you do them matters, too, or at least it does to me. I do SubQ (not IM) which means smaller needle and little to no pain. I barely notice it going in most of the time. I also opt to do my shot after a hot shower, when i'm relaxed, and i do it at night so i can go right to bed. It's sort of becoming a routine for me.
Though i will admit that if i stare at the needle long enough and really THINK about the fact i'm about to give myself a shot (even though i know it doesn't hurt at this point) i will freak out and have to stop, re-start, etc.
Good luck!