Each case is unique. In a lot of cases it will be an allergic reaction - could be to toothpaste, lip balm, something in your diet (wheat, dairy, etc). Your best bet is to replace your toothpaste with something organic. Stop eating wheat and dairy products to see if that helps - also, take note of when your lips start to burn, especially after eating a meal. Replace your lip balm, AND Vaseline, with pure shea butter (L'Occitane sells this product). Start using shea butter products for your entire face care regime.
Get a low percentage cortisone cream (0.5%) and apply a tiny amount to your lips when you wake up and before you go to sleep. If you have a really severe case, apply a tiny amount after meals also. Do not go crazy with this ointment! And do not use it for prolonged periods of time. If your irritation doesn't start to get better after a week, go see a dermatologist - you might need to be prescribed antibiotics.
Good luck to all of you! I can firsthand agree that this is like going through hell.