to work up = generate?

This is a good question! Generally, I would say that you can only work up an appetite, a sweat, or (less frequently) excitement/enthusiasm. There may be others that I can't think of, but the first two are the primary ones. I'm not sure why this is, but I think part of it is that you only work up things within yourself, usually through physical labor or exercise. Things internal to you. So you should not use "work up" to mean "generate" more broadly. Something like "I'll work up some money for that game I want to buy" does not work. This is not to be confused with "to work someone up" which means to make some one excited or angry. As in "he got all worked up when I told him he'll have to stay late". As far as grammar for your sentence goes, I would say "I had worked up **a** sweat. I don't think this is because there's a particular grammar rule, just that the phrase "work up a sweat" is so commonly used that it sounds strange without the "a".

It can mean that (among other things), but my experience is that it implies that the thing being generated is quick to generate and not necessarily final. * "Thanks for the information; I'll work up a quote and send it for you to review." More informal. We expect comments requiring a modification to the quote. * "Thanks for the information; I'll generate and send a quote for your review." More formal. This is what I'm telling you it costs based on the scope of work. Period.

The phrase is "work up **a** sweat." It is used for something physically generated in your body through repeated action (or inaction) and can also be used with "an appetite" and possibly other similar phenomena. It doesn't make sense in other contexts.