I don't remember the name, but I think I know which infection you are talking about. It can be removed with certain malware removal software. You don't have to lose your computer or even necessarily the data on it.

In general, never trust any phone number or email address or link provided in an email or pop-up message -- no matter how legitimate it may seem. If it claims to be coming from your bank or credit card company, pull out your last statement and call the number provided there so you can be sure who you are talking to. Then ask them if anything is actually amiss with your account. Ditto for any other organization.

I hope this provides some re-assurance.