yes please do sit up straight - especially at your age you can prevent arthritis which you'll really not appreciate when you get a bit older.
wish i had someone say to me at that age 'sit up' !
i'm having physio at the moment and they give exercises that can stretch and strengthen those muscles around the spine to support it (could find some diagrams on some websites ?)
and swimming is a great way of the water supporting your back when exercising without causing any pain.
mind you, sitting up is good but dont stay that way for too long periods as the muscles tense up - maybe try 'shuffling' your back when you feel sore now and again - just to alleviate
another thing the physios encourage it the 'core-struture' where the whole posture of your back can be healthy (that will be somewhere on websites too)
if its really hurting you & your concerned then visit your doctor and asked to be referred for a x-ray (hopefully it will rule out anything)
best of luck & look after yourself :)
