Is Retin-A cause of cracked corners of my mouths and my burning tongue?

The first thing that came to mind as I read your question was the possibilty of a B12 or folic acid deficiency.  In fact there are several nutrients that when low can cause the symptoms of a burning tongue. 
Theoretically tretinoin/retin A could cause a burning sensation but you would have to get it directly on your tongue and even then the saliva is going to dilute and wash most of it away (unless you have dry mouth).  I've never heard of retin A migrating into the mouth.  Make sure you are not accidentally licking the area and avoid peri-oral application for now.
The cracks at the corners of the mouth could once again be related to nutrients, candida infection or early actinic keratosis (among other things) as well as retin A.  I would recommend seeing your primary doctor to rule out systemic causes of your symptoms. 
Hope this is useful information for you.  Best,
Dr. Amy