Recently I sent an e-mail that contains my resume to a company that I want to get my internship with. The problem is the e-mail name is not professional and goofy. Should I resend another e-mail using another account or just wait for their reply?
Just wait for a reply. The chances are that many interns also use informal email addresses for correspondence, so this wouldn't be entirely unexpected. If the tone of your covering email is professional, this should be fine.
But yes, try to obtain a less goofy email address going forwards. Although many employers won't really mind, it comes across better when you give people your email address.
A good example of a professional-looking email address would be email@example.com