Your check engine light can come on if you don't tighten your gas cap after fueling. Look in your owner's manual to see how many clicks you need to turn it. After a day or so of driving the light should go out.
If not, you should get it checked out. It may just be a coincidence that it came on after you got gas.
As for the swaying you're feeling, you may want to have someone put the vehicle up and check the suspension components. Hard to tell without looking at it.
〉 Answered on Feb 21st, 2012 by Lori Johnson, Owner and Instructor at Ladies Start Your Engines