Being pregnant myself, I know all too well the increased need to urinate while pregnant. I believe this is due to increased fluids in the body, as well as the weight of the fetus on the bladder. Pregnancy alone can be enough to stretch out the pelvic floor muscles and lead to stress urinary incontinence (although it's important to note that women who've never been pregnant, as well as men, can also experience stress incontinence). However, it sounds like what you're experience is more of an urgency to urinate, or an overactive bladder, rather than incontinence due to weakened pelvic floor muscles. I wrote a sharepost a while ago about overactive bladder that you might want to read.

I personally haven't learned of pregnancy or childbirth playing a role or being a factor in overactive bladder or urge incontinence. I would see a urogynecologist about this problem so that they can diagnose you properly and help you find some relief.