Some good advice here already, I would say read through this thread and make a little list of all the suggestions. Try to rank them in terms of what is easy to do and what is harder to do. Make the easy changes immediately. Choose a few of the harder changes and commit to putting time in on them
I will say that at age 16 I was a little overweight as well. I think I peaked around 5' 10" and 230lbs. For me I was able to lose quite a lot of weight just with small changes to my diet. I committed to eating only 3 square meals a day with no snacks, no soda, and always including a fruit or vegetable. Sure, there were times when everyone around me at a party was eating chips or cake or something, but I got good at saying no. The weight fell off pretty quickly and I was down to like 165 a year or so later.
You're lucky in the sense that losing weight is easier when you're young.
And beyond that, I would recommend a good workout program. Don't focus on trying to become shredded overnight. Don't fixate on your abs or any particular glamor muscle. Just put in your time developing strength in every part of your body. It will help your overall performance and help to prevent injuries. Start light. Do your PT every day. Ask the PT if they can help you with create a full-body exercise program beyond just rehabbing your current injury. Truth be told, good fitness is way more valuable in preventing injury than any particular size/weight ratio. Strong muscles protect your bones.
Be motivated by your desire to skate and do other fun shit. For me working out isn't really a ton of fun, but I know it will help me surf/skate/snowboard more effectively. That makes it easy to be motivated, because that's the stuff I really want to do.