The front of United's cabin is Economy Plus, as the other poster explained. Were you hoping for a bulkhead seat for a bassinet? United says they're suitable only for babies up to 6 months so your son is probably too big. Also, United prioritizes the bulkhead seats for their ff's, not families with small children.
I've flown long haul on United many times in the back of the plane and honestly, it wasn't a problem at all. In fact, it was convenient being close to the lavs back there.
I have a daughter who only has to look at a car to start throwing up (like when I was little). We're just a very, very motionsick prone family. Only once did a child throw up (and that was kind of borderline "spit-up" frankly). I've had kids throw up on the way to the airport only to be fine on the flight itself (though it's not really an ideal way to start a journey).
Having said this, here's what you can try. Call within a week of flying and see if they can change it. If not, call 48 hours prior. If not, request yet again at check-in. You might get lucky. Once at the airport, when they saw that my husband was in business (on a separate reservation), they moved us to the very first row that wasn't E+, all four of us, just so that we would be physically closer. I didn't even request this!
I would not count on anyone switching on the flight itself. Passengers always say no to Flight Attendants anyway (experience speaking).
Yes, the back is bumpier but in the economy section, it's really not enough of a difference to worry about. Try to get forward and if not, relax. The slight extra movement might even help put your son to sleep!