Diane A
Looks like early paronychia, look that up and see if that fits. Try hot soaks and antibiotic creme. If not, you will need to be seen.
GF
Looks like toe nail is damaged and toe is enlarged. You injured that toe and the nail is cracked. It may fall off, but don't worry. I had 3 toe nails fall of in 1 night from a bad pair of work boots.
Wash your toes and clip the nails please