First of all you need to realize why the lips are burning and itching in order to get rid of the discomfort. Have you recently kissed someone with sores on their mouth or inside the mouth or performed an oral sex on someone?
It could be herpes. Before an initial breakout of blisters (which may not even show up in the initial breakout), herpes starts to itch, burn, hurt and cause redness. If you had any contact with anybody who had herpes (it could be friendly kiss on the cheeks as well since herpes is passed in skin to skin contact).
Other causes include skin disorders like contact dermatitis, eczema, psoriasis but it could also be some kind of allergy.
I would advise you to see a dermatologist and have it evaluated. Don’t kiss with anyone until you see a doctor.
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If you have or suspect that you have a medical problem, promptly contact your physician or health care provider.