If you’re logged in with the correct credentials, nothing should look different. If your order history or membership status seem off, that means you most likely logged in with the wrong email.
If you use an Apple device, check to make sure you didn’t use the private relay feature that generates an email address with @privaterelay.appleid.com when you registered with Shipt. If you registered with private relay, but logged in with your real, non-Apple email, you wouldn’t see the same account history. You can find more information about this here.
Regardless of how it happened, it’s a quick fix: just log out and then back in with the right email address.