Kennedy's high school roommate used to joke, "If I ever wrote a biography [about him], I would call it John F. Kennedy: A Medical History." He certainly wouldn't be lacking for material. But as Kennedy's actual biographers tend to agree, perhaps the only thing more impressive than his medical records was his determination to deal with it in private and get on with public ambitions.
Among Kennedy's most serious and multifaceted health problems was Addison's disease (adrenal glands not doing their job), officially diagnosed in 1947. But it wasn't the first one that threw a major wrench into his life--that was probably a severe form of colitis, for which he spent months in the hospital undergoing tests in high school. It's medically possible his treatment for that actually contributed to the later adrenal and stomach problems, and potentially even worsened his disabling back pain. The medications did interfere with his body enough that his doctors suspected he had leukemia at one point.
One way or another, his Addison's didn't develop from one of the usual pathways--tuberculosis--which allowed Robert Kennedy to assert on his brother's behalf in 1960, "[He] does not now nor has he ever had an ailment described classically as Addison’s Disease, which is a tuberculose destruction of the adrenal gland." Well played.
It wasn't just JFK's family that labored to keep his health problems hidden. Throughout his rising political career in the 1950s, Kennedy's back pain grew more and more debilitating. He started using crutches to walk, but being sure to hide them in the car when he gave campaign speeches "erect and smiling, looking as fit and healthy as the light heavyweight champion of the world." But by 1954 he needed the crutches to get to the stage, and finally even just to stand. To deal with this, he chose to undergo two major spinal surgeries--despite Addison's raising the risk of deadly infection and anesthesia complications so much his family begged him not to do it. And...yes, it nearly killed him.
And when the surgeries didn't work well enough to let him walk without crutches, he turned to physician Janet Travall. She prescribed injections of Novocaine and procaine, but also the use of adaptive technology--a rocking chair rather than a regular desk chair, a special reading platform/podium for speeches. This helped. Robert Caro, in fact, follows his sources in describing the shots for back pain and better corticosteroid treatment of Addison's underlying a transformation in Kennedy's physicality in the later 1950s that moved from health to charisma, certifying his political ambitions to the highest office in the country.
...But Kennedy was still suffering from frequent GI problems, bad back pain, and the side effects of all the drugs he was on to combat the first two. During Kennedy's early months in the White House at least, he received regular visits from shady doctor Max Jacobson, whose standard bedside aide included injections of a combination of more painkillers and amphetamines. (My earlier answer on the portrayal of John and Jackie Kennedy's drug use in The Crown might interest you.) Eventually, White House doctor and admiral George Burkley managed to squeeze out Jacobson and Travall. With the aid of, of all people, Kennedy's endocrinologist (for the Addison's), he convinced Kennedy to work with Dr. Hans Kraus on an intensive physical therapy regimen.
...And as you might expect, Kennedy agreed to the program of exercises, massage, and heat therapy only under the agreement that it be sold to the public as a means to take the president's health "from good to excellent."
If I have not convinced you that JFK was one tough cookie, I recommend Robert Dallek's An Unfinished Life: John F. Kennedy, 1917-1963. He includes lengthy excerpts from Kennedy's own writing describing his various stomach and intestinal problems, which I won't repeat here. Instead, I'll just share a screenshot of the book's index entry on "Kennedy, John Fitzgerald (JFK) - health problems of." It is the longest single subheading. The second? "Kennedy, John Fitzgerald (JFK) - medications of."
...You know, I have some health issues, but...if you need me, I'll be over here, never complaining about any of them again.