Sounds like it. I don't think it's going to be $100. Maybe $60-ish?
You could have them leave it slightly larger so you could grow into more later. Get more use out of it.
At some point, you'll buy your own suit in the future. Another way to go is to buy that suit now, but it sounds like it's done already. It probably doesn't matter. An extra suit won't hurt later.
You'd have to get a suit tailored a little bit with whatever you got most likely. The less tailoring, the cheaper, of course. The less 'invasive' the tailoring too, the cheaper. Shortening the sleeves is easier/cheaper than ripping the back apart.