My friend contracted mono awhile ago and is still sick with it, before i knew i had shook his hand and after i found out i washed them. can i get it?

Maybe/not: You did the reasonable thing, washing hands can reduce your risk. Many adults are already immune to mono having had it as a kid when it is often mild & rarely labeled. It is passed through saliva during the active phase and your contact might have exposed you, but in a minor way. It will be up to 4-6 weeks before the incubation period has passed & you know for sure.