Say what you mean and mean what you say.

He should have done it not because you are a woman but because you were sick.

But you chose to be passive aggressive so you sort of brought it on yourself.

You cleaning up is your own fault. You told him you'd do it. Don't play mind games with people, it rarely works in your favor. plus, you put it outside without telling him, can't blame him if he didn't know it was there. So let the cleaning go. In the future, use the very good advice you've received.