Should i stay home from school with a cold?

I have a really bad contagious cold, no fever just continous coughing, sore throat etc. i caught it from my mom, now my dad has caught it from me. Tomorrow i have a socials test before lunch, and after lunch i have PE, then badminton practice after school. Should i just stay home the whole day, or leave after i take the test? cus i know running outside in PE cl will just make it worse.