Yes, I would try using a different Lightning address. (I’m not familiar with bitrefill’s configuration, or I’d try to troubleshoot that too).

Alby is an easy (but custodial) solution, as is Wallet of Satoshi (if you’re outside of the USA).

Also — adding a Lightning address is only the receiving part. To send zaps… it depends on which client you’re using. But most will either “open” your Lightning wallet, or, if the client supports NWC (Nostr Wallet Connect), you can integrate certain Lightning wallets directly with your nostr client.

It’s a lot of info, so just ask if you have any questions!!