As you had skin symptoms after coming in contact with the
cat,so allergy to cats cannot be ruled out.In the last trimester
of pregnancy,
cat allergens cannot pose a direct risk to your baby but it may effect fetal well being by causing allergy symptoms like skin symptoms,hives,itching,respiratory symptoms to life threatening anaphylaxis in the mother.
I would suggest that you get rid of the cat as far as possible.If not possible then,use reputable allergy avoidance products throughout your home.