Peter, this sounds like what I just went through in Costa Rica. If so, it's an infection of the eyelash follicles (basically a stye) and will go away on its own over time. You can help it along the way by cleaning the eye lids regularly with a gentle soap. And some websites recommended putting moist teabags on the eyes, but who knows about that. Also recommended was coconut oil.
If it gets extreme, you might get a prescription for an anti-bacterial topical cream.
If it's a stye I would definitely recommend an antibacterial cream, I had one with my daughter that lasted 4 months, then when we used the cream it went away in a week (of course you need to finish off the course).