tire out of round,
brakes sticking on a wheel
Certain sections of poor paving can do that. I have had vehicles that did not drive well on roads that have too much slant, too many trucks over it, many little things, even the weather and also with different loads of people and "stuff" on the vehicle.
Could be you lost one of the weights used to balance the wheels. No problem as long as you drive slow. Just get it rebalanced . A few dollars if you can tell which one. More if they have to do all of them
It started shaking because it get scared to be on the same road as real cars! It thinks it is a tough guy on side streets, but is out of it's depth when amongst real vehicles.
I stopped and checked to see if I had a flat but the tires were all full. I started it up and drove slowly and it didn't do it again.
