Can you contract covid through your eyes even when you do not rub them?

Yes all you need is to get enough virus in the conjunctiva that the body does not knock out. I would think. Having the Vacc should boost antibodies to help kill the virus.

Yes, transmission is believed to be through droplets with eyes being accepted as possible port of entry.

Although it is not likely to be a major cause of transmission, COVID-19 can infect the conjunctiva or any mucous membrane. For this reason, among many others, you should practice good hand hygeine and not touch your eyes.