You absolutely should change your password if it is provided to you - it should have been the very first job you did on receipt. What an individual password gives you is security that somebody else cannot login and sent emails under your account
Don’t think that resetting the password prevents your emails being monitored, accessed and read though it is usually a condition of provision and use that email traffic ‘may’ be monitored
It sounds like you need some pretty elementary training or discussions about email policy - does your council have an IT or communications policy? If yes, that’s your starting point