a gaming mouse is not necessary but if you say that your mouse is cheap, you could get a better one but if a normal mouse fits your need, then i don't think it's worth paying twice the price for something that does the same thing but if you really want a gaming mouse then go for it, you will be satisfied.
^+1 I wouldn't say a gaming mouse is necessary however I don't think playing (especially shooters) with a 6$ mouse could be really enjoyable. The perks of good gamine mice are:
They usually have a high DPI so you can take the sensitivity a lot higher than normal or cheap mice. You usually have some extra buttons you can customize (really comes in handy in fast paced games). They are obviously built a lot better than cheap mice and are usually more comfortable to use.
So to sum up: you don't need a specific gaming mouse however I think you should get something better than the cheapest mouse you can possibly find.
For me, a gaming mouse isnt really neccesarry but they tend to be build better and offer some better features and and shaped to your hand, in most cases. Mousemats (gaming surfaces) are relatively cheap see below for what i just ordered: