The money was on hold on my account said to be withdrawn end of February. ... Is that how it normally works?
No, that is not how it normally works. Credit card holds typically only last from 1 to 7 days, but it sounds like the hotel is attempting to put a hold on your account for a full month. Furthermore, why did they charge the CC now instead of the end of February? Since it sounds like they messed up, they should take the necessary steps to reverse the charge immediately, which typically takes just a few days to clear.
Although hotels are generally known for taking a long time to process refunds, I believe this is an exceptional case because they made a mistake. IMHO they should bend over backwards to fix the mistake ASAP.
That being said, If the amount charged isn't affecting your ability to use the card as you normally would, I'd probably just wait out the 21 days and not worry about it. I'd put a reminder in my calendar to check on day 22 and if the money isn't returned by then, I'd call my CC provider and file a dispute. In fact, I might call my CC provider now and explain the situation to make sure that they agree that it's OK to wait before disputing.