I cut my thumb while cutting raw chicken. could this lead to salmonella going into the bloodstream and effecting other organs?

I've never heard or: encountered this in 35 years of clinical practice, but I suppose it is theoretically possible. Many rare events would have to coincide: the chicken was actually infected with salmonella; the infected part came in contact with your cut; there was enough of the bacteria transmitted to actually infect you. All of this is highly unlikely. Stay well:)