2 weeks on Retin-A. Is it true that it's better not to use oily moisturizers? (Photo)

I'm using a whitener but my face has gotten dark and discolored. red and lines i never had before. sticking it out to find out if retin a works. I read that oil isnt good with retin a? Is oil the reason why the areas around my mouth look brown? I also read that retin a is its own moisturizer and that moisturizing makes natural cells lazy and stop working since they see we have already moisturized., the cells do not. Is this true?