What word can I use to describe the small lump on the skin seen after a mosquito bite?
Technical terms aside, the most common phrase used to describe this is just mosquito bite.
I got a mosquito bite yesterday. It really itches.
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.)
A rather general way to describe any such skin protrusion is a swelling.
If the pain and itching are gone and the swelling minimal, then the term "bite-mark" would be what my dialect would dictate.