GOsh sounds like you might have moved to our road, although further up where houses have back gardens onto the road, as opposed to the front of the house.
We bought our house over 9 years ago (edge of market town, A-road, 30mph limit, driveway separating us from road) and we didnt even consider the road noise being a problem - pre-kids we both were out of the house 8am-6pm during the week and literally never noticed any road noise until 3 weeks during high summer when we wanted to sleep with bedroom windows open - it would've been fine except for a few lorries rumbling past in the early hours.
I do admit to noticing the road a little more often now - work part time, 3 young kids. But we still don't consider it a problem - if I am ever having a 'the road is annoying me' phase, I just remember that we honestly couldn't have afforded our large, detached period property if it were just one road back from our road. Plus, a few houses have come on the market on our road this summer and have all sold within a week, at full asking, so when people say they're difficult to sell, it doesn't seem so on our road at least.
How 'busy' is 'busy' though - our road is a steady flow of traffic at 8-9am, then 5-6pm, but goes really quiet (or what we consider quiet!) other than those times. Some main roads are a nightmare, others aren't so.
You've got a lot going on at the moment - new baby, new house, its no wonder you're feeling worried/ have I made right decision etc. I imagine in a months time, you'll have forgotten about the road noise (or new baby will drown it out anyway
)
defo look into secondary glazing though - have it on both our bay windows at front of house, and really worth it.