If you could clarify what you mean with "this weird thing in my throat" maybe we could help more.
If you are straining your vocal cords, be it by improper technique exceeding your range or too long exercising, it is normal to feel a sort of "itching" in your larynx. But usually it is not solved by coughing, but rather by "clearing your throat". Some teachers do not recommend doing this, or if absolutely necessary, to do it very softly.
You may also produce some phlegms that could have been there already, but are set loose by the vibration and cord movements.
Some people sip water periodically when singing (me included), but others prefer other drinks such as gatorade or similar while others nothing at all.
If you smoke, you may be experiencing problems related to this habit and you should have your lungs checked by a doctor. Even if you don't, it could be a good idea to have a chest x-ray evaluated by a specialist.
I study singing in a private school and have never met a colleague coughing when singing. For this reason I think it is not "normal" to cough, unless you are ill (for example suffering a bronchitis).
A peronal suggestion is to avoid singing in a smokey environment. I know that this is sometimes impossible to achieve, but if you suffer when inhaling second hand cigarette smoke, then it could be a very serious problem for developing a rock singer career.
In my case, I simply could not imagine singing in a smokey room. I lose my voice almost instantly.... I am not saying that this is it is a common or frequent problem, but it is my actual and personal experience.