Headaches with this unilateral distribution may need further investigation by your docotr or possibly a neurologist. These may be cluster headaches as one possibility. This is a vascular type of headache but distinct to a migraine type.A type of inflammatory disoder of arteries ; namely temporal arteritis might also need to be ruled out.
Cluster headaches are usually severe and one sided. These may also be associated with tearing of the affected side.
Temporal arteritis might might cause headaches and can affect either side but may be more involved on one side. Checking blood inflammatory markers>>C-reactive protein and sed rate would tend to be very elevated if this were the cause.
Either of these would require specific treatment strategies.
I hope this information is helpful for you. If you have further questions then i will be happy to get back with you. If my answer has been helpful and to your satisfaction then please remember to press the "ACCEPT" button. Thank You and Best Regards,
Anthony Bray MD
No I would not expect skin changes with these except part of what you describe sounds like some flushing and this might occur with cluster type headaches.The flushing and more prominent appearance of the veins would correspond with increased blood flow to the skin.These I think fit more with possible cluster type headaches. The sense that you feel one side is oily and has thicker skin is an atypical symptom which does not fit neatly into any of the common headache categories.
I hope this helps. Further questions are welcome if you have others. Best Regards,