Your photo shows where you have caused damage. The darker red spots is where the skin is thinner which is why you can see the blood capillaries underneath. I have rip lines from years of biting/ripping at the lips which you don't have, so you need to stop causing damage to the inferior part of the lip to avoid causing this as it will only take longer to heal them.
You should be mindful to leave your lips alone and let them heal and maybe apply a healing ointment ( I use coconut oil).
Do not lick your lips under any circumstances, it will dry them out more and cause them to crack and bleed.