I have received a lot of bounce-back emails for emails I didn't send

This can mean that a spammer has gained access to your mailbox and is using it to send spam emails. There are two main ways this can happen: either the password can be guessed by brute force, or it can be captured by malware on a computer it has been used on. You should change the password to something strong and unique immediately and also run antivirus and malware scans on any computer that has been used to connect to the mailbox.