Sink not draining correctly

I recently install a new bathroom sink/vanity. The drain pipe was 1-1/4" and I wanted to have a clean out at the bottom on the trap. The problem is that none of the hardware stores that I go to had 1-1/4" trap with a clean only 1-1/2" so I use and 1-1/2" and went down to 1-1/4" before the drain goes behind the wall. Now when the sink is filled it doesn't drain right. Do you think by doing this I caused the issue or could there be another issue.

The size of the connection at the wall determines how quickly or slowly water passes through that connection, and that connection neither knows nor cares what size trap precedes it. I would guess your sink seems to "not drain right" when it is full simply because it seems to drain faster when it is only half full even though the rate of flow is essentially the same in both cases. Personally, I find the typical 1-1/4" trap simple to disassemble and remove for cleaning or to recover a ring or the cap for the toothpaste tube, and I would rather not have an easy-access cleanout plug somebody else might leave loose under a bathroom sink.

The reduction in size is improper, but NOT the cause of the slow draining. You may have installed a "vessel sink" which almost always drains slow, or the pipe in the wall could be partially obstructed.

Like hj mentioned, if it's a vessel sink without an overflow, the grids could be slowing down the water. vessel sinks with overflows drains much better.

Or it could be that the p-trap was not trimmed in length at the wall.
Or that you need to clean the drain.