Could the two of you agree to working together (or in parallel) on the cleaning for a few set hours a week or even half an hour a day? Another thing that worked for me in the past was to split up the tasks----(and change it up now and then)---sit down and each take responsibility for certain routine tasks for, say, the next month or two....eg: doing dishes, taking out trash, cleaning the bathroom...)
This would make it something you both work on....the financial equity may change over time but the housework will always be there. It is only human to bring up perceived/actual examples of "I do this...you don't...etc" when upset. The thing is to prevent the upset from happening.