Hello, I would like to know if in order to fly to Mexico I need to present the proof that I have given the injection for the covid? or only a face mask and antibacterial gel and antibacterial wipes are required

The face mask is mandatory. As for the rest of it you will need to call your airline directly.

I just got back from New York. They never asked for any proof. That is a different country.

You should check with Mexico and see if they have any requirements of people traveling across the border. There seem to be stricker rules there than domestic travel. Possibly you may only need a negative test.