This computer is already associated with an Apple ID.

Issue with iTunes Music Accounts

I have two iTunes music accounts, one based in the US and the other in HK. Recently, I logged into my US account to download some old purchased music. After downloading the music, I switched back to my HK account, but iTunes locked my account and displayed the message, "This computer is already associated with an Apple ID. You can use iTunes Match on this computer with just one Apple ID every 90 days. This computer can be used with a different Apple ID in 76 days."

I need to download my purchased music for both personal and work purposes. However, I am unable to do so due to this issue. Is there a solution to this problem that does not require me to wait for 76 days?