Pain at the back of the head during press ups?

When I'm doing press ups, when I get close to the 20th press up I get an incapacitating pain of the both sides of the back of my head nearer the neck region. I have to stop. This pain takes about 20 minutes to recede and it is very strange and painful. What is it and how can I stop it, thanks. By the way, I'm breathing quite a lot so I don't think its that.