Don't worry, Mena. I'm pretty sure you'll adapt to your public school in no time. You seem like a great person, so I'm pretty sure you'll find friends very quickly.
Maybe it's just me, but I guess changing from a private school to a public school is almost like moving. I had to change schools, around 5 years ago, because I had to move. I was so nervous, because all of my old classmates were back in my old town and I basically grew up with them also. As for now, I'm not doing so well in this school even though I've been here for a couple of years already, but I'm sure your outcome will be different and better than mine. I know it's scary and hard to adjust, but we all have to go through and accept these little changes in life. I'm sure you'll do fine. Good luck.