Hi, with PC mic, you can only do so much. Quite limited, but what do you expect from something which less than a dollar to manufacture.
It's pretty ok actually, as these are normally tuned to the vocal range of frequency, except its not linear at all.
An advise to get the best of it. Find the sweet spot, and volume to sing at. Means you have to train your voice to it. Because at a certain position and singing volume range, that's where you get the best sample.
Unlike an enclosed studio with a very sensitive condenser mike, where you can accept a very wide range of possible sample which is easy to doctor.
Other than that, my advise, be content. What do you expect for a few dollars mic, others pro ones uses mikes easily cost several thousands per piece.
You can also upgrade to trademark Shure SM58 as a next step possibilities, cost about more than $150. (do not get used ones, may have lost sensitiveity after long use or abuse)