Have to agree with the majority of posters here. A spill isn't something that's particular to flight or travel, it's just something that sometimes happens.

However, if something you own was damaged/needed cleaning then you surely could ask compensation for that. I don't think that happened, though, so what remains is that it's clear you felt that it smelt very unpleasant and who knows it might actually have distressed the baby (a tiny bit on top of the distress of air travel itself). Good to hear that he's doing fine, by the way, that's the most important thing!

The upshot is that at worst you can classify this as inconvenience. Asking/expecting for anything more than token compensation, like some Aadvantage miles or a small-sum travel voucher, would be too much. Basically, it would be nice of American Airlines to recognise that you did not have the best experience and give them a chance to turn that around.

However, in the end, in my opinion, they owe you nothing.