@docsgirl, not all items are prime eligible. Those that are prime will clearly indicate that. If you are not seeing the prime logo try logging out then logging in. It is possible that you were not automatically signed in as a prime member immediately after signing up for the free trial.
A caveat about the free trial. If you have any doubts about remaining a prime member watch your dates closely because Amazon will automatically charge you the membership fee without a grace period.
What is good for the goose today will also be good for the gander tomorrow.