I used a hand sanitizer with alcohol and then i accidentally touched a small part of the skin near my eye (but didn't rub). i washed my hands and face after, will covid transmit like that?

A 70 percent isopropyl alcohol solution or more is effective against most bacteria & fungi & many viruses. If the alcohol concentration in your hand sanitizer is 70 percent or more you should be relatively safe. Frequent hand washing with soap & water for at least 20 seconds is also effective for Covid-19. So continue to maintain very good hygiene. I wish you well with your health!