Nothing you've said suggests any problem with your phone. It sounds like someone has hacked your account, which if you use a weak password, or the same password on many sites (one of which has poor password security and gets hacked itself), and don't use 2-factor authentication, can happen even if your phone is completely secure (except, of course, if someone has your GMail passwork your phone is no longer completely secure).
Change your password (use a secure one that you don't use anywhere else), enable two-factor authentication, check your Google account's security settings to see what devices have accessed it and de-authorise any that you don't recognise.