I recently have experienced the same symptoms of the weeping, yellow crust on lips
It started with cracked, chapped lips
applied Blistex to help heal my lips
. Only my lips did not heal. They started appearing swollen, with reddness on inner lips, yellow crust on tops of lips, no pain but about as uncomfortable as a badly chapped lip.
On the 4th day I went to go see a doctor; he diagnosed me with a condtion called Impetigo which is a bacterial infection that is very contagious.