After the first day, heat will help speed healing. For pain relief, steer clear of aspirin, which thins your blood and will increase discoloration. These potions may ease the pain, itching, and swelling, and they're certainly better than gritting your teeth. Add some as you cook and consider blending up a juice concoction with fresh cloves of garlic. For a persistent or severe sore throat, however, be sure to see your doctor.
Sprains involve ligaments and usually include swelling and discoloration.
Use your ice pack, on and off, for a couple of days to reduce swelling and ease the pain. Strains happen to muscles and don't produce swelling or bright displays. For strains, heat helps most, because it increases blood flow, which speeds healing. In either case, gentle stretching will help get you up and moving sooner. Don't get them in the first place.