I would get chills from Betaseron. Aleeve would help.
I am on copaxone and last year, spent the whole year crying I was hot! sweltering hot! turn down the heat! This year, im cold! I have an extra heater in my room, and I put on long sleeve Tshirts, and wear a sweater round the house. I wonder if they changed the formula. I know being hot was MUCH worse. I would rather be chilly, but it seems there is no happy medium with this stuff.
As your body adjusts to the meds, you will settle in. Hang in there.