as a muscle group, unless you are doing exercises that stretch your abs out, such as reverse back bends etc., you are very unlikely to overwork your abs to the point of injury. doing lots of situps will not hurt you; that's not to say you won't feel it, because you will at first, but once you are over that preliminary hump of "ouch my abs are pretty damn sore" which takes two or three weeks, you can really make some headway there
edit: i've been where you were with the curls by the way, it is a miserable feeling and can be incredibly painful. to avoid that feeling, after curls stretch out your elbow joint extensively. this is especially important if you are doing curls for reps. just grab onto a nearby bar, horizontal preferably, and hang off of it. you'll feel a lot better afterwards