I was recently diagnosed with a sinus infection. I have been taking 2 mg of amoxicillan a day. I am scared of getting a blood clot. Should I get up?

Get up. Sinus infections or taking Amoxicillin would not increase your risk for a blood clot. Immobilization does increase the risk. At least keep moving your calves. Get up if not at risk of falling. Why you are in bed?
Yes. Nothing about sinus or antibiotics that should make you immobile. Blood clots can occur if trauma, cancer, dehydration, hypercoagulability, stasis-sedentary unusual if none of these and moving around.