Can you get sick and if so what are the symptoms from a stray cat scratches and it broke skin?

Possible infection.: If a cat scratches you, it can introduce bacterial infection into the skin causing an impetigo or even a cellulitis. If there is redness, pain, swelling or frank pus at the site of the scratch, especially if it is worsening or spreading, seek medical assistance immediately. You will need at a minimum oral antibiotic therapy.