I'm concerned about my email/this site too. As far as I know H can't log onto this pc, since he wiped his stuff off when he got one. However, he is more tech than me, so for that reason I wouldn't trust him. I know he hasn't got time to snoop on me but I'm very careful.
Stop beating yourself up NOW. It's not your fault it's his fault, he took a risk.
I think you can password protect access to you email but don't know any more than that. Also I set up an email with yahoo which is password protected and I'm assuming he can't open that?