I don't understand why Bittrex would be telling you that you have logged in from a private IP address. A 192.168.x.x address should never be used on the internet. The only way you could be accessing Bittrex from this address is if you were on a LAN or similar with their servers, which I suspect is not the case.

Are you sure you are trying to log in to the real site? You are potentially entering your details to a phishing site and they are sending these emails to the email address you just entered as a way to try to prevent you from realizing what you have done.