Dry ice in a cooler is no problem for carry on, I had a friend bring a carry on sized foam icebox with Blue Bell back to California. TSA will just have you open the cooler so they can see whats inside. UA won't even bat an eye onboard. The hazard for dry ice and lithium batteries in checked bags is that no one is monitoring in the cargo hold.

That said I've also brought a fresh deep dish on board and it causes more problems as everyone wants some.