This is not a regurgitation. I'd wait a week before offering another meal, though, as the whole experience sounds unpleasant for your snake and you don't want to set up negative associations with feeding.
I am going to gently give you a bit of a hard time, though, because I am struggling to understand how you could be uncertain if a meal you offer your snake is completely thawed or not. If the rat felt 'a bit stiff' you needed to check it before offering. If you are genuinely wondering if the cracking sounds you heard were like an ice cube in warm water, then we really need to review your procedures for thawing and offering food.
I'm serious. This could kill your snake. Before you feed your snake, you HAVE to be sure the rodent is completely thawed. It needs to feel soft everywhere. You should be able to freely bend it. It should not have any trace of cold anywhere.
Please, please review your thawing procedures and be absolutely certain that the food you are offering your snake is 100% thawed, because if you end up with a real regurgitation to deal with, the consequences can be serious. Yes, I am pressuring you here but it's because I know you care about your snake - you posted here because you want information and support, and that's a good thing!