My computer crashed but I had my bitcoin address and password in my password manager so I thought I was good. I installed the Bitcoin core app again, but can't figure out how to open my existing wallet and realized the password I have isn't the seed-like sequence of words I thought it was. Am I screwed?
We had a different name on that but the same meaning, that is a mnemonic phrase, or they called the 12 words seeds phrase or must be known in the name of a private key. Upon creation of a wallet, you must write it down on a sheet of paper to have a backup of your wallet anytime even your computer used was crashed or damage. So now, without the private key, you can't able to open your wallet, it should have a password and the private key must be kept safe.
Try to explore on this board,
Beginners & Help, there's basic information regarding Bitcoin wallet there on how to create and how to recover your wallet through your private key or seed phrase.
Anyway, welcome to the Bitcointalk forum, here, you will learn a lot, and next time you were handling Bitcoin with proper knowledge of storing your crypto, a digital asset.