How can i stop biting the skin off my lips? is this a sign if anxiety?

Depends: Are you aware of doing it? If not, it could be from malocclusion (bad bite) to physiologic reasons.. See your dentist... You have many minor salivary glands on your lips, if you traumatize them, you may get mucoceles... See your dentist.

Most likely: As they say, go with your gut feelings. The fact that you suspect this habit as a response to anxiety, leads me to believe that you are correct in your assumption. If you find your lips itchy, cracking, swollen, or covered with any lesions, then there may be some other underlying cause. Either decide to stop by finding another outlet to occupy your thoughts or see a dentist for an evaluation.

Possibly a BFRB?: This sounds like a body-focused repetitive behavior (bfrb) - like hair pulling & nail biting. Bfrbs can arise in response to (a) emotions (anxiety, fear, boredom, excitement); &/or (b) sensing rough areas skin (like cracked skin on lips). Bfrbs can feel pleasurable & can serve 2 relieve tension. Effective behavioral treatments available. A clinical psychologist who specializes in bfrbs can help.