The green Success message and not receiving any error messages is a very clear indication that CF7 is sending the email.
So your email is probably being spammed somewhere in the email process.
Emails can be considered spam for a whole host of reasons and get rejected at many points in the email process in addition to your spam folder.
See Contact Form 7 Email Issues - this links to a much more comprehensive article which also covers emails being considered spam.
See also Best Practice to Set Up Mail.