If you were sent the invitation to join a Premium for Family plan, and your account shows active in the plan admin's account but you can't use Premium, it's possible that you have more than one Spotify account and you accessed the wrong one by mistake.
In this case, log out and log back into your account. If it's linked to FB, make sure to use the Log in with Facebook option. Otherwise, use the username or emaill address registered in your account.
You can find more tips to help you locate your other accounts here.