After taking medications, will my eye swelling and my proptosis at least go down?

Maybe. Part of what makes the eyes appear abnormal is that the eyelids are pulled back; this gets better with treatment. Inflammation around the eyes will also generally decrease once the thyroid levels are normal, but if there is a lot of soft tissue buildup behind the eyes, they may continue to bulge out. Surgery can be done, especially if the bulging is causing double vision.