What would cause my foot to swell like a sprained ankle?

Foot swelling: Many causes: sprain, fracture, contusion, infection, strain, edema, pvd, vascular insufficiency, among others. Check with your orthopedic or foot doc.

Assuming you : Did not sprain it, an infection, an insect bites, a sunburn, gout, an allergic reaction to name a few...

Swelling: Other than a sprained ankle, reasons could be gout, infection, arthritis, tendon tear, ligament tear, instability to ankle, defect to ankle joint cartilage, foreign body in joint, stress fracture, fracture, hypertension, kidney disease, charcot arthropathy, etc. Good luck.