The side of my lip is chapped and torn!

The side of my lip is chapped and torn!

I do apply lip balm as part of my daily routine, but
Maybe it's because the weather is still so dry these days, but my perpetually dry lips are bothering me and even hurting~😭
Especially next to the lips (you probably can't see it well right now since I have Vaseline on),
The sides are all torn open, so this lasts a long time.
It’s not just dry; sometimes my lips crack and bleed. I think it’s because my lips are so dry...
Should I go to the doctor for lips like these that are cracking? ㅠㅠ Honestly, I feel like I've been putting off going to the doctor for too long.
I was wondering if there is any medicine or prescription ointment available!!

It does feel a little more moisturized after applying lip balm, but... ㅠㅠ How to care for lips and the sides that repeatedly crack, and good solutions for this situation *Dermatologist prescriptions or surgical prescriptions?? ㅠㅠ etc.
If you have experience fixing this, I would appreciate your recommendations.