My daughter has major bladder problems and as a result has chronic UTIs. She has had many accidents in private and in public. The biggest problem is that, like you, she has no notice whatsoever. She uses 'Depends' when she doesn't want an embarrassment.
She has also used Detrol LA to decrease the frequency of urinating. This works really well, but does have side effects that can be problematic, so she just uses it for travelling or other situations where she needs to decrease the frequency or guarantee no accidents.
Don't be afraid to discuss this problem with your doctor.
My heart goes out to you - to be so young with these kinds of problems just doesn't seem right.