A red spot on the white of the eye is often a benign condition resulting from a broken blood vessel, called a subconjunctival hemorrhage. This can happen for no reason or can be a result of straining such as a cough or lifting weights.
It is usually pain-free; however, mild stinging and tenderness are possible but uncommon. If yours hurts a lot, the red spot may be a focal area of inflammation in the eye called episcleritis or scleritis.
If your vision is not affected, I think it is safe to wait a day or two to see if the red spot starts to resolve. It may take longer to completely resolve, though. If it gets worse, enlarges, or becomes clearly associated with pain or decreased vision then a consult with an Eye M.D. is necessary.