I cut my hand with my finger nails and now it itches and it is slightly risen and red. I rubbed it with alcohol and put antibiotic. What is it.

Inflamed or infected. This could be a simple urticarial response where nobodies white cells are producing histamines causing the itch… It could also represent early or superficial infection…if it becomes painful or produces pus you may need a stronger antibiotic by mouth.