possibly but wen i was that far along that happened to me and it turned out i had a uti i woud have ur dr check
At 12 weeks the baby is still pretty small however your uterus is expanding and growing and can definitely put pressure on your bladder. Most mommies get a little relief in the 2nd trimester from the uterus shifting away from your bladder but the feeling will come back again torwards ur last trimester. Try laying and different positions. I had the same problem in the beginning.
It could definately be the baby, my lovely little one loves kicking my bladder lol.