One reason pain is worse at night when not moving around is because of how the pain fibers are set up.

There are 4 major ones each with varying degrees of insulation/myelination. From thickly insulated (and therefore the fastest) to no myelination which are the slowest.

This link explains better:
Neuroscience For Kids - conduction velocity

The C fibers are very slow and will be unable to get your attention as the A-a fibers are the fastest, and get priority over the other 3 because the biological system evolved to do so.
We have to have constant attention to where we are in space, and moving either slowly or quickly. This is called proprioception.

The C fibers also are divided up, into heat receptors and cold receptors. Cold ones subsume the hot ones, and that is why cold
helps pain, and also why menthol helps topically for PN and minor pain. Menthol is a biochemical stimulant of the cold receptors.

So when you get up in pain, and walk around, that is what is happening. The burning is still there, but your proprioceptive A-a fibers are getting all the attention.

There are topical things you can do... There are topical lidocaine containing products to rub into inner and outer wrists. Apply Aspercreme Lidocaine lotion/cream to your wrists and top of the hands and go up the arms a bit if necessary.This may take down the burning you are having. A little goes a long way. Don't apply to the inner hands, because the skin is too thick there to let much lidocaine in. The nerves enter the hands at the inner wrist
at the carpal tunnel. You can experiment with the inner hands, and depending on how thick the skin is on your palms it may work or not. I have good results with applications at the inner wrist myself.

Aspercreme Pain Relieving Cremes and Gels: Pain Relieving Creme with Lidocaine

Avoid hot baths, showers, hot tubs, heating pads, saunas, steam rooms, as these trigger the heat sensing nerves, and create a pain cycle that is difficult to break.

Did your chemo involve injections into your arms? It is possible that nerves there were damaged by the drugs, or even the blood vessels. Years ago I had IVs containing Aldomet a blood pressure drug. When I had my C-section, during the recovery I had terrible pain in my arms, and swollen hands etc. The doctors then said that Aldomet caused a vasculitis in my veins. I still get mild tingling in my hands (they called it a residual carpal tunnel), but it is not severe or everyday. I can live with it. I have braces to wear if I overdo gardening or using my wrists with tools, etc.)
But after my C-section it was over a year before I was mostly back to normal with my arms and hands. I do recall that after the surgery, my arms were worse than my abdominal incision which was a long 15 incher!

Yes the chem drugs are a main cause of neuropathy. Even more so I would think if they leaked out of an IV into the tissues where the needle resided. Statins for cholesterol and fluoroquinolone antibiotics like Cipro and Levaquin are huge offenders as well.