My yahoo email account got hacked into. I changed my pword. Is my email and computer safe now?

Yesterday an email got sent from my email address but I didn't send it. My computer was off at the time it was sent (it was early morning and I was still sleeping and I live by myself). I found out about it because people were like "what was up with that email?" and I was like "what email? i haven't sent anything" So then I checked my email and saw that there was an email in my sent folder that went out to my entire contacts list and it was like a spam email of a link to a site selling male enhancement. No one knows my pword and I've never had any problems like that, but just the night before I was using the internet at the local starbucks which is obviously a public unsecured network. I never use any unsecured networks but my air conditioning broke so I had to get out of the house since it was so hot. So I suspect that someone or some program hacked into my email account over that unsecured internet connection. I changed my pword from a different computer (on a secure network) and then I ran a full sweep of my anti-virus on my computer and nothing was detected or found so there is no virus. So was changing my pword all that I needed to do? Is everything safe now?