can skin cancer develop under finger and toe nails?

I have recently noticed a small, reddish-brown spot under the nail of the big toe on my right foot.  It is not on, but under the surface of the nail, and irregular in shape

Yes it can.  My mother developed a lump under her fingernail which turned out to be cancerous and had the end of her finger amputated just above the second finger joint.  She is fine now and the cancer had not spread, she still goes for check ups and did not have to undergo chemo or radio therapy.  It took a lot to persaude the doctor to have it looked at and only after removal of her nail and a further biopsy did they do anything.