Nope, it is not okay. You cannot go up after the trap. And, the kitchen can be tough to alter, since most kitchen sinks have windows over them, what is coming out of the wall is usually just a horizontal trap arm that runs to one side of the sink or the other and then the drain drops down and the vent goes up. You cannot just cut into the wall where the pipe comes out of the wall and lower that piece. The entire horz trap arm, the san tee, vent, and drain connection would have to be lowered.
Code does allow a 4" trap seal, so if you are close, you may be able to get a trap with a deeper seal, but otherwise, it is really usually quite an ordeal.