You can check your last account activity to see what devices have logged into your account, when and from where. This should give you a pretty good idea whether anyone has access to your Google account. It is a straightforward process:
“To see activity for your entire Google Account, go to security.google.com and click Recent activity under “Security” on the left. This page includes security-related actions you’ve taken, like signing in to your Google Account, changing your password, or adding a recovery email address or phone number.” https://support.google.com/mail/answer/45938?hl=en
If you think that someone has installed some kind of monitoring software on your phone, the simplest and most effective thing to do is a factory reset. This will erase everything and return the device to the way it was when it left the factory. Make sure to backup everything before you do this, or it will be gone forever. If you decide to do a factory reset, it should be in your settings under “Backup & reset,” although this varies somewhat from device to device.