Nobody gets into a United Club just waiving just a credit card. Not sure why you think it would be different at an outside lounge. At a United Club, a United boarding pass will show that it's linked to the United Club membership provided through Chase, not because it's linked to a Chase card.

Please bring the app up. Log in. Go to your profile, go to account, go to your wallet, and scroll down to "more wallet items". The United Club card you need should be there if there's no issue. Quit listening to phone reps who have no clue - you are wasting your time if they say all you have to do is wave a credit card around. You can't. I have an Infinite card. The UC membership card provided by having the credit card is in the app wallet.