Of course a 15 year old can love.
I believe you - even if others don't!
But, still - you are 15 and respecting your parents and her parents is the best thing to do.
They do sound pretty strict, but they don't sound horrible. At least you get to talk to her on the phone and stuff.
If you've been friends this long already - and you're only 15,... you could indeed try just being friends with her again...if the relationship as it stands doesn't suit you.