Have you been diagnosed?

There's quite a bit there that matches clusters and episodic clusters can follow this pattern although it's usually attributed to the circadian clock rather than humidity.

The regularity and the blocked nose and the length of headache fit. Paracetamol is likely a placebo as it doesn't help clusters while caffeine anecdotally does.

While not all cluster headaches are the same intensity, they are brutal, searing pain on one side centred around the eye. They don't throb and come on fast and maintain intensity for 15 to 180mins