This sounds very painful! Split lips are not usually a major medical problem, but they can be a nuisance and they can take quite a while to heal up completely.
The major cause of dry or chapped lips is mechanical irritation - most commonly, this means excessive licking or picking of the lips. Unfortunately, once the lips get irritated and dried out, the reflex is to constantly moisten them with the tongue. However, this repeated action actually makes the irritation worse and dries the lips out even more!
In other words, it is important to break the cycle of repeated moisture and friction. You can do this first of all by making a conscious effort not to lick or pick at the affected area. Also, you can use a good chap stick, preferably one with menthol or other soothing agents in it, as these agents can decrease the itching and burning sensation that drives the urge to lick the lips constantly. Apply the chap stick at regular intervals throughout the day, and you should start to see a difference within a few days. Keep applying it, however, until the skin is completely healed up.
If this issue persists, you should go see your primary care doctor
for more advice.