Do a search for 'angular cheilitis'. You should get a bunch of threads with info and advice. ; )

Take a Vitamin B supplement. It will help to clear it up. Also use lots & lots of paw-paw cream on your lips at night & try for a few days not to open your mouth very widely as they may scab a little when they are healing & you don't want to keep ripping that scab off.

I think that Aquaphor works better than Vaseline. That was my experience, at least. Carry some with you and smear it in your mouth/in the corners a couple times an hour. Also, drink a TON of water. The same thing happened to me, and whenever I was really conscious about constantly drinking water, they would heal up. Anytime I slacked on that front, my lips cracked again.

polysporin

1% hydrocortisone cream (not gel) was a life-saver for me. I bought Cortizone 10 and applied it to the cracks at the corners of my mouth (morning and night). They healed within three days. Nothing else (e.g., Aquaphor, Vaseline, etc.) worked at all. After the initial healing, I only applied it when I felt the corners of my mouth were getting dry enough to crack (they'd start to feel kinda sticky) and stopped a couple days later when they felt fine again. This proactive application prevented my mouth corners from cracking for the rest of my course. I wish I would have tried it earlier!

It is a fungal candida infection and needs to be treated with an anti-yeast cream like Lotrimin; hydrating the area is going to further the yeast growth.