If there is burning on application of Latisse, chances are you have some inflammation of the skin of your lid margins which is being irritated by the Latisse or its vehicle (what it is mixed in). This suggests that you may have blepharitis or eczema, or a skin condition which makes you sensitive to it. You may also be allergic to the Latisse but this would more likely cause itching. There is also the possibility that you are rubbing too hard with the applicator and it only needs to be gently applied.
It would be worthwhile to discuss this with your provider and have an exam of your eyelash margins by an ophthalmologist to rule out any other medical conditions.