Coughing up mucus with traces of blood. Swollen tonsils and throat. Is the blood likely just due to coughing breaking the blood vessels in throat?

Yes. Excessive pressure from coughing can break capillaries and cause small amount of blood to appear in the mucus. Take a probiotic (Megafood Megaflora Plus brand), zinc 50 mg/day (NOW is a good brand), Vitamin D3 10,000 IU/day (NOW brand) or sunshine for 30-45 minutes at noon daily to get over the the infection faster. Throat coat liquorice tea (consume several times/day) also helps to reduce pain.