I would seriously suggest that capsaicin makes burning worse in the long run.

Phenytoin is on drug lists that cause PN! But then alot of doctors don't know that.

There is a new topical cream/lotion by Aspercreme that is 4% lidocaine. That used to be RX but now you can buy it in most stores. It it wonderful and just a small amount covers a large area. I find it as good as the RX patches, and it is affordable.

You could rub some on the thighs and it may work all day like it does for me. There is a condition called meralgia paresthetica which affects the sensory areas of the thighs. This is an entrapped nerve from the lumbar region, and you should be tested for that.

Read this link entirely... there is an illustration (figure 2B) of where the nerve originates in the lumbar region, goes thru the abdomen, and exists from under the inguinal ligament to travel to the front and lateral side of the thigh.This sensory nerve does not affect the muscles or strength.
Hip Pain in Athletes - American Family Physician

I had this following abdominal surgery when I had a C-section. It only affected by right thigh, but it can affect both, especially if
some disc compression is occurring in the lumbar vertebrae.
I used lidocaine patches for mine after many years of suffering.
It went into remission after two weeks (which surprised me) finally, so I don't have the thigh pain anymore.

The OTC product:
Aspercreme Pain Relieving Cremes and Gels: Pain Relieving Creme with Lidocaine

It is worth a try, and not expensive. You only need a small amount on each thigh...say 1/2 a quarter's worth on each side.
Rub it in well, and let dry.