Well, first, we need to know these are bruises -- do they hurt when you press on them? It could be some kind of rash.
A bruise can develop when you do pushups excessively or do not take breaks between workouts. This can place extreme or repetitive pressure on the muscles, cartilage, bone, tendons and ligaments in the arms. You also can develop a bruise if you fall or jam against the floor or another object while doing pushups. A bruise also can be the result of sprain or strain which occurs when the muscles or ligaments in the area tear or pull with sudden changes of direction or improper form.
You need to rest for at least 2 days! You should be icing on and off for 20 minutes. If after 2 days you see no improvement
then I suggest seeing your Dr.