When you blow your nose you are creating some slight increased venous pressure within your body, similar to what we refer to as a Valsalva technique. This increased venous pressure is transmitted to the veins and venous sinuses around the brain resulting in this temporary discomfort.

You may be blowing pressurized air into your sinuses producing the pain. Consult an ENT for examination and possible CT scan of your sinuses to rule out other possibilities

Probable barotrauma to sinuses

When you blow your nose you force air into your sinuses. In an otherwise
normal/healthy sinus, the air just comes right back out. In an inflamed
and partially obstructed sinus, you may force air in and that air may have
a hard time getting out, leaving a positive pressure in a given sinus.
This may be uncomfortable. Other explanations may exist, but this seems a
likely one in this case.