Ask an Eye Doctor and Get an Answer ASAP
It seems to be blepharitis. It is inflammation of the eyelids. Since Self-care measures using warm compresses doesn't work well, you should go to the urgent care to have exam and topical antibiotics, steroid, cyclosporine if it is blepharitis.
Another possibility is the infection started to spread. It is called cellulitis. You should go to the urgent care.