Last night my class went to a ski trip. i did snowboard/tube. i fell twice while tubing. on the way home my left arm felt sore. what should i do?

Rest, ice: If just your arm, and you're only experiencing soreness, then i would rest the area, ice for 20 minutes 2-4 times/day and consider taking advil (ibuprofen) at a dose of 400 mg (2 otc pills) 3-4 times/day for 2-3 days. Take with food. According to your history, you also have dizziness and a headache. If you hit your head, then you could be having concussion symptoms. Consider seeing a doc if this is the case.