"Normal" means a wide range of things, but yes, what you feel is normal. When full, the bladder backs up against the bundle of nerves commonly known as the "G" spot. The pressure stimulates the g-spot.
You can orgasm by sitting on the toilet and stopping and starting the flow of urine rhythmically. A lot of girls masturbate this way. I certainly did before I bought my first vibrator!
You can also enhance partner sex by holding your bladder and using the pressure to help your lover find your G-spot.
Holding your bladder during sex is also good because peeing afterwards helps flush out bacteria driven into your urethra during intercourse.
Enjoy.
Where are the pains?