So I have 2 accounts on steam, one for my games, and one for CS:GO. I accidentally put the CS:GO account instead of the other one, and after doing so did I realize it. So I disconnected from my account and tried logging in with my other one, but however many times I try it just says account conflict and won't let me log in. Is this a known bug with a fix?
If so what can I do?

I honestly don't know, as I don't have another steam account in hand. But I went to Setting -> Steam (disconnect)
and when I try connecting again, it showed me the steam login interface (attached). Can you get to that? If so, when you then login with your desired account, would that still not work?

If still not, then it sounds like a bug to me, worthy to report it.