Noise after new tires

Welcome to 2CarPros. It could be the tires. The tread patterns and materials used can make large differences in the amount of noise you hear. It's also possible that the act of lifting it to change the tires moved the suspension into areas that it hasn't been in a while and it's causing a rough ride because the struts and other parts were moved a lot.
A quick test to see if it's the tires or suspension is to drive on different road types and see if the rumble changes or goes away if you drive on concrete, pavement, dirt or gravel. If the noise is there on concrete but goes away on pavement or dirt then it's likely the tires.
The rough ride is harder to test for. You might want to look up the tires for their reviews and see if other people have similar complaints.
Did you alter the tire size or rim size at all? That can make a drastic difference in noise and ride quality as well.

You may want to take it back to the shop and just have them check things over. It could be something as simple as a wheel weight came off or shifted. Or possibly one of the tires has gone bad. I have seen new tires that were not round or that had defects and started to fail within a few miles.
It's also possible it could be something unrelated like an engine or transmission mount that decided to fail now and you feel that when the engine moves around. To check if that could be the problem open the hood and have someone hold the brake with the car in gear, then step on the gas to make the engine move against the mounts, it will normally move some, maybe an inch or so with good mounts, if it moves 2-3 inches or more then your mounts are failing.