Can you get a finger infection if you touch smelly moist dog treats? they leave a smell on your hand (i washed my hands now im scared to take a shower?

No risk, no worry. You've also asked about other no-risk situations, such as a dusty room. You may be germaphobic, i.e. excessive or irrational fear of infection and contamination. If such thoughts or fears are frequent, get professional counseling. Germophobia can be a sign of later serious mental health disability. In any case, a shower would reduce any risk, not raise it further.