For a 2nd grade ankle sprain with no fractures, should I use crutches or is it enough to wear an inflatable stirrup ankle brace? Or should I use both

See below. If you can walk without pain with just the brace then you do not need crutches.
Your body will tell. If it is too painful to walk on, use the crutches.
2nd Grade Sprain. When there is a second degree or second grade sprain there is a partial tear of the ligament. Sometimes that will include two of the primary ligaments on the outside of the ankle also known as the lateral side. With a sprain there is small nerve damage that it causes the ankle to become unstable. It is the instability that is the problem because you are now prone to more injury. Follow doctor's advice.
Camwalker antherapy. Many times ankle sprains are under treated. A second degree would benefit from a camwalker for at least one week followed by physical therapy.
Whatever you need. If you are comfortable putting all your weight in the leg then that is fine. If not then use the crutches until you are. Start working on gentle range of motion exercises now and then strengthening in 7-10 days. Once the swelling is down, you may want to switch to a lace up type brace which is less bulky and more functional.