Having had some eye surgery done in my time related to my tear ducts, here's what I know about USA emergency eye stuff from a day I needed it and my surgeon was on vacation states away:

ER's will always have an ophthalmologist on call. Basically my surgeons nurse was like either they can have the on call suregon (1pm on a Monday) get him into his office on an emergency basis or we will send him to the ER and have him called in. She was like you can go ask him what he'd like to do.

Urgent care, on the other hand, will not, in my opinion, have an eye specialist around so they may be able to look at it, bill you and send you to the ER or they will give you some antibiotic drops and you're fine.

Right now I'd suggest a warm compress and see what happens. Use a washcloth and get it very warm with damp water.