Being skinny or not has nothing to do with being a good dancer or going to a dance class outside of school. That remark was just plain ignorant. It is dance technique and proper training that matters. Ballet doesn't make anyone skinny in spite of the fact that professional ballet dancers are thin. Truth is that is how they were born. Ballet will however tone and elongate the muscles with proper training.
That being said, you may or may not be getting a full dance class at your school. The other girl may also be getting lousy dance classes where she attends as anyone can call themselves a ballet teacher and teach ballet with little or poor training.
A full dance class is 90 minutes long. It has a 45 minute barre, followed by the next 45 minutes both in the center and then ending with across the floor. If your teacher is properly trained and can pass along that training that is what matters most. If your teacher is just a gym teacher with little ballet training from a recreational school then that may be problematic.

Source(s):

My daughter is a professional dancer. I worked for NYCB (New York City Ballet)

Dance move ideas for summer by Calvin Harris?

I have a group of 5 and we are dancing to summer for a school project. If you have dance ideas or dance references we can use could you suggest them below? I'd like for us to do something cool like with partners and one does something different, or something thats easy but actually complicated. Or something we could do altogether that would look cool. THANKs

You should not be feeling pain doing an arabesque. My guess is your form is not correct causing you to compress your spine. This is best addressed by working with your teacher.
I am including a video that shows the mechanics of a proper arabesque and shows what happens when you focus on turning out the working leg and end up compressing your spine and get results like you have been having. I hope you find this clip both informative and helpful.
(Starts :40 into clip)