What word can I use to describe the small lump on the skin seen after a mosquito bite?
I would call this a welt. My impression is that this word is reasonably common and would be readily understood, much more so than weal.
Oddly, as tchrist pointed out in a comment on another answer, the OED doesn't really have this definition. The closest seems to be welt, n.1 definition 4c: A ridge on the flesh, esp. the mark of a healed wound; a seam. Could this be a British-American divide? (I'm a native American English speaker.)