What causes swollen uvula and redness in back of throat?

Infection etc. The swelling process found is equivalent to inflammation which will take time to resolve.
Throat infection. The most common cause is an infection of throat like strep throat, mononucleosis, and a variety of viruses. Only strep throat is treated by antibiotics and i see you are on the antibiotic, augmentin (amoxicillin and clavulanate).
Inflammation. As your body fights an infection, the tonsils (back of throat) are one of the major trafficking sites for your immune system to recognize and fight off infections. Generally, redness, swelling is a visible sign that the cells in the area are releasing cytokines (chemical communications) to cause your blood vessels to dilate and immune cells to slip through and infiltrate the involved tissues.