Cause And Cure For Deep Cuts On Lips

I've got this deep cuts at both my lips, like splits.
It started after alcohol and sunburn last summer, it went away of it self and came back with vengeance and it's still there, i've tryed all kind of oils " just making it even worse" and a couple of anti-fungals and cortisone, but it doesnt seem to work.
Also tryed to change whole diet to extreme low carb for some time and see if it would heal, but no.
Also tryed adding vitamin B and Iron but nothing.
What should i do?
Been to doctors and they say just put vaseline on it, but it just makes it worse.Really frustrating cannot even talk smile or eat properly, and it looks horrible.