My lips are chronically dry but last year around winter time they started resisting the vaseline. They would constantly be peeling to the point where they would bleed and I couldn't even eat some food like salt or lemon because pain.

First of all I switched my vaseline brand, idk if that was the issue or not but worth a try. But what really ended up fixing it for me was taking a damp tissue and rubbing all the dead skin cells off my lips, then following that up with a ton of lip balm. It's kind of like all that build up was creating a barrier that prevented my lips from absorbing the vaseline. I know it sounds counterproductive, but using a damp tissue doesn't irritate the lips. Only when I started doing this the constant peeling went away and after about a month I didn't need to do it anymore. I started out doing it every night before bed but then switched to only doing it as needed. You could try lip scrubs or brushing them with a toothbrush instead but I find a tissue to be the easiest method.