Upvote:2
I'm sorry, but odds are you'll have to go back to Sri Lanka and apply for a new visa.
Except in "exceptional circumstances" (which means getting hit by a bus, not applying for the wrong visa), Schengen Type C short-stay visas cannot be extended beyond 90 days or converted into other visas.
The general rule is that new visas have to applied for in embassy closest to your place of residence, meaning New Delhi for Sri Lanka.
I would still talk to the place you are studying and see if they have any better ideas, since you're probably not the first in this situation.