Handled raw chicken while cooking with a small cut on my hand - washed afterwards with antibacterial soap and alcohol. will i be ok?

Likely will be ok: If the small cut (in a healthy person) was not deep enough to need "closure" by a doctor, it should heal up just like any other shallow small cut on the skin. If it looks too reddish, is too tender, is swollen, or is oozing stuff, a doctor can check for infection. Adults should be up to date on tetanus shots, which means having a Tdap shot (contains whooping cough protection) in the past 10 years.