I understand your concern.
As per your description,with short term history of cough,sore throat,white lump in mouth,cough chances of oral cancer are less.
However smoking is main contributing factor in oral cancer.
Heavy smokers (more than one pack a day) are at a 24 times higher risk for oral cancer.
Oral cancer is more likely to strike after the age of 50.
Oral cancer can appear as a lump or ulcer in the mouth more than 2 weeks that may be
A deep, hard-edged crack in the tissue
Pale, dark, or discolored
Painless at first, then a burning sensation or pain when the tumor is advanced.
In your case,it's painful.
So it doesn't indicate oral cancer at present.
You should see your doctor if it'll persist more than 2 weeks.
Hope this helps.