Mine started just like yours, dry chapped lips that picked and bit.3 years down the line i found out that it was a staph infection. I've had a few rounds of Antibiotics but because i had the staph for so long it's going to take a while for it to go. But i don't get any crusts or hardly any buildup at all. Just the skin takes a while to heal.
My advice is to go to the doctor and have a swab culture. I heard doctors are expensive outisde the UK but it's well worth it.