Your height is all preprogrammed in your genes before you were born, unless you have some physical/metabolic dysfunction that affects that part of the growing process. I don't think at 16 your established height has yet been achieved. You may still get another inch before you're 20.
WE do loose height throughout the day. We are tallest in our early day hours and the body settles by the end of the day. If you drive, you'll notice the rear view mirror may need adjusting after a day of activity.
Any exercises or stretches on a chin up bar won't achieve permanent height. But, if you are in good shape, especially your back and stomach, with good muscle tone and excellent posture, you will look taller. We do loose height through aging, especially if our backs are in bad shape through injury. I've lost a half inch since I was 16. At that time, being female at 5'8 was very tall. Not today!
There are surgeries that some people with dwarfism have done on their legs and arms to achieve a more "normal" height and body proportion. But, I don't think that 5'10" would consider you a candidate for that.
Calcium in milk will keep your bones and muscles working well and strong. Lifting weights also keeps bone density in tact.
Teenage years are a time of change (physically, emotionally and perspectively), of independence and anticipation of adulthood. Don't loose your perspective of who you are by focussing on things you cannot change. Acceptance of who you are will not be changed by an inch or two. I think that 5'10" is actually a perfect height for a male.
Best to you,