I'm 20 and I too have had these symptoms and have still got them exactly the same and know exactly how you are feeling.
I went to the doctors in late August due to excessive frequency at night and in the day with 'urge'/full bladder feelings but not leaking or anything like that.
I was first told I had an infection in August, given three, maybe more different types of antibiotics. Went for regular urine sample testings and they all came back clear after 3 days worth of antibiotics over the weekend but they still insisted on prescribing me more antibiotics rather than getting to the exact cause of the problem. I then asked my doctor to send me to see a urogynaecologist. The urogynaecolgist said that my problems are not due to the infection. I had Staph B infection and he said that many women can walk around with this infection not even knowing that they've got it as it usually doesn't cause any symptoms or problems.
He has arranged for me to have a urodynamics test which I'm unfortunately going to have to wait for quite a while to even get which is getting a little frustrating as I just want to be normal again.
I would certainly recommend that you ask your doctor to send you to either a uroggynaecolgist or a urologist for further in-depth investigations to find out why your bladder is like it is.
Hope this is of help to you and good luck.