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First, I recommend that you promptly change your Email account password. If you didn't send the messages then there would seem to be three immediate possibilities:

1) Someone is spoofing your Email address. That should be easy to prove because the IP won't be correct for the sending Email server.

2) Someone has access to your Email account. Unfortunately Email account passwords are normally sent in plain text meaning they are easy to steal. If you've used a public Internet portal to access your accounts that is fraught with danger. If you use a WiFi network at home it is an absolute must that encryption be enabled. Even better restrict the network MAC addresses that are allowed to access your network to only those you have.

3) Someone has access to your computer. Work for example.