Stoicism can absolutely help you. Your frustration is understandable, but from my perspective it seems a little absurd. You can still sleep over at friends' houses (although as an adult it's typically visiting someone in another city or crashing after drinking too much). You can still go see movies. What's stopping you?
It sounds like you're complaining about "growing up too fast," about not getting to goof off and be immature. Being an adult doesn't prevent you from goofing off, and skipping quickly through immaturity was probably more of a blessing than a curse (even if it takes you another 30 years to realize it).
Or maybe you're angry at your mother and sister for neglecting their responsibilities? They will always be themselves, and you cannot control them. Best accept who they are and make the most of it (as you already have!).
Don't worry about not having teenage friends. A vanishingly small percentage of those friendships last very long. Adult friends tend to be the ones you keep.
As for the Stoics--they considered duty to be very important, especially duty to family. They would've likely considered your sacrifice to be very noble, and an indicator of strong moral character. Taking care of your sister was absolutely the right thing to do in your situation. Why do you regret doing the right thing?
If this sounds hollow, then stop being responsible. Go have fun. I guarantee it won't make life any more meaningful. Most real meaning in life comes from accepting responsibilities and performing them well, especially when it comes to other people. But you're still young, probably too young to agree with me. You'll have to figure all this out for yourself.