Adobe doesn't stash your password on your PC, that would be terribly insecure.
Just reset your password, it won't require you to reauthorize anything.
Although,
IF you are only using ADE for library books, why bother? I just authorize ADE without an ID since I just use it for library ebooks. I will not lose my computer within the 2/3 week loan period, and it works just fine as long as I don't expect to use it on a different computer, which I don't. You can even transfer to devices, without being authorized with an Adobe ID.
The only thing I have EVER gotten out of having that Adobe ID I registered in the impetuousness of youth is spam from when they just got hacked. I never used the multiple-computers thing, because frankly, I never buy books through ADE.
You will only need to be authorized with an Adobe ID if you expect to need access to
purchases down the road.