Mr_T
Challenge Tour Pro
The simple answer is yes, there is no reason why you couldn't.
The complicated answer is maybe, I don't want to try and put you off but as previously mentioned its an incredibly tough profession to crack, you need to be able to devote a lot of time (which you seem to be doing
) Devoting this much time could have a detrimental effect on your school grades, I would say its equally important if not more important to get good school results as not only will that stand you in good stead for the PGA exams but if for whatever reason it doesn't work out you'll have something to fall back on
If you're doing gcses like me then you'll have loads of time to practice and play in the summer, so If you put the time in that handicap could really fall by the end of the season
If its what you want then go for it! 
Also in terms of lesson prices a set of lessons cost me 100 quid and I got 5 with a 6th one free, I would be very suprised if you were looking at more than 100 quid for a set of junior lessons
The complicated answer is maybe, I don't want to try and put you off but as previously mentioned its an incredibly tough profession to crack, you need to be able to devote a lot of time (which you seem to be doing
Also in terms of lesson prices a set of lessons cost me 100 quid and I got 5 with a 6th one free, I would be very suprised if you were looking at more than 100 quid for a set of junior lessons