Go for your dream.. If your eyesight doesn't meet the grade, you will find out soon enough, don't let it disapoint you if it isn't, but don't believe a doctors view of 10 years ago when you were growing put you down now.. Doctors get it wrong still.
Yeah, go to uni. Areonautical degrees are pretty useless unless you want to work for BAE or a Type 21 company or ENGO management (and experience is as important for those). Mechanical Engineering has more outlets IMHO, if the pilot route doesn't happen.
Go and do UAS if you can.. It will give you an insight to the type of people who will progress.
If you apply, do your homework first before applying.. Officer first then Pilot second.. The Pilots trade is known as GD(P).. The GD stands for General Duties!! The leader of men in battle and peace.. Airborne Warrior is only part of what you will do, if you get through the hurdles first!
Good luck.