Usually this type of symptom is a result of an external cause such as irritation from shampoo, permanent, or hair coloring. Some patients who are receiving chemotherapy also experience scalp tenderness and burning.
You mentioned to Vicky that you were not experiencing hair loss, but I found a study that showed these symptoms to be a precursor to hair loss. An allergy could also cause these symptoms.
You mentioned hypertension, but you did not mention if you were taking anti-hypertensive medication. Adverse reactions of this nature to anti-hypertensive is rare but possible.
You may just have very sensitive nerves to the scalp. The pain you feel is very real. You should begin your search for a diagnosis with a dermatologist; you may then be referred to neurologist.
Burning discomfort may be related to the trigeminal nerve. This involvement occasionally precedes the appearance of herpes vesicles; Herpes zoster, in the early stages can be mistaken for temporal arteritis. Temporal arteritis is also known as Giant Cell Arteritis.
I wanted to check some online resources to cover as many possibilities as I could. I did not find any significant information, however I did find the following in an exerpt on Giant Cell Arteritis (Temporal Arteritis) from "THE MERCK MANUAL".......
"A condition called giant cell arteritis in older patients who present with headaches, or scalp tenderness. Giant cell arteritis is also known as temporal arteritis and cranial arteritis is a disorder that results in swelling of arteries in the head (most often the temporal arteries, which are located on the temples on each side of the head), neck, and arms. This swelling causes the arteries to narrow, reducing blood flow."