If you plan to start hormones, no, it won't magically solve your problems. It's a process and you have to do a lot of other things to pass. Of course, we will never have a fully functioning cis-male-like penis - I don't know how far you're looking to transition, but that's about the only thing you cannot achieve through current medical standards and whatnot. But yeah, I've been on hormones for about 11 weeks now and a lot has changed about me - my voice has dropped significantly, facial features are starting to masculinize, more muscle definition, some fat restribution....yeah, things like that.
I mean, I had a pretty male presence before deciding to transition though I've known I wanted to be a male since the time I hit puberty and became sexually aware - that was around 10-11 years old. I knew surgeries were possible by age 12, but didn't know much about hormone replacement therapy until about 14. I don't know how I found this out - probably the friends I made on the internet, because I was living in a pretty conservative rural community at the time. For instance, I like girls. That was enough for most people to talk about me like I had the plague in my town - well most of my peers at least.
My family used to poke fun at trans-issues too until they actually understood them. Of course, my dad was never really passive or dismissive about me advocating for the LGBTQIA community. He supported me liking women, and my mom does too (though she didn't as much initially). The trans thing is an entirely different ballpark though - and for a long time, I would start to accept myself, be ready to come out, tell a couple of friends, then my dysphoria would act up & I would slip back into denial. Just so you know, that's not a healthy thing to do about yourself. At all. Oh also, they come from Catholic background, but aren't religious much at all. Honestly though, my parents never rejected the fact I was more masculine - I was more scared of them rejecting me wanting to transition. As a child, I naturally was drawn to more "boy oriented" concepts and would not be swayed otherwise. They were used to that - I'm not sure that your parents are yet, but you will need to explain to them in detail how you feel about yourself as much as possible so they can start to understand. Make sure not to feel attacked if they respond poorly - actually, to avoid them reacting poorly, tell them from the start that they are free to ask you any questions, as long as they are well intended, because you want them to understand and for there to be as little as possible confusion. You do have a sister who supports you, so depending on your age, possibly she can be of help to you as well. Are you close? Does she know more about your life and how you feel about the world than your parents do?
My sister was not supportive of trans-issues at all before I decided to come out. Things are okay with her now, but she is still the most apprehensive family member compared to my mom and dad. A few years back she called trans surgeries "stupid" and said that "people that have problems if they want to do something disgusting like that to their body". I had to correct her and tell her that a lot of thought goes into those surgeries; they just don't decide over night that they want to transition, and it's almost not even a choice - they feel like that's who they are and that she was in no place to judge. Of course, this was actually me standing up for myself, but no one knew that at the time. She hadn't been intolerant after that incident, but she was sort of neutral about the issue. We never really talked about it much because there is no LGBTQIA community in the town she goes to school in. She's actually a year older than you, I believe, because she turned sixteen in August.