A few things you can check out:
What's happening in your From: header? Why do you have two email addresses crammed into the <> brackets there? - Youcan use multiple addresses, but they must be formatted the same way the mail() manual entry explains the to field must be formatted.
Emails usually use Windows style line endings: \r\n . - Perhaps not particularly important these days, since modern email clients don't really care, but still worth getting right.
You aren't capturing and validating the return value of the mail() call. It returns a boolean value indicating whether not the mail was accepted for delivery. You should always capture and check it, and if you get FALSE make sure to show/log an error instead of just blindly showing the normal "thank you" page.