The max money you can hold is 99,999. The shop lets you sell stuff to a value higher than that, but any money in excess of 99,999 is discarded.
I haven't hit the inventory cap yet, but it's over 4,000. (Edit: it's 9999.)
Also, the title is kind of a turn-off. Are we fighting COVID or something?
Playing anyway to see what UMAs have to do with lung disease.