Additionally to the pressure points indicated by @AlejandroVicaria, I find it useful to massage the points / areas highlighted in the picture below. In my case, I get headaches in case of air drafts (e.g. car's air conditioner), and the most useful is the areas on the sides, around the ears.
Some practice will be needed, to find the right spots.
Also, please consider visiting a doctor, just in case. You may have heart problems, blood pressure problems, and I would not exclude teeth problems - see a dentist also. It is better to be safe than sorry.
Even though it is not always possible, try to have a ventilator around. Even if it blows to cool only your feet / legs, your entire body will thank you. The blood gets cooled down in the feet / legs, and then travels to the brain somewhat cooler. It will not work miracles, but it is still better than nothing.
You mention washing your face often. Keep doing it. If possible, don't wipe all the water after that. Wash you arms also, if possible. If you wear short pants, apply some thin layer of water on the legs also.
Some people claim that you should shower with hot water during hot weather. After the shower you will feel the environment cooler. You may look into this too, to check if it works for you.