It could be this one:
John Q (2002)
starring Denzel Washington, Kimberly Elise, Daniel E. Smith, Laura Harring
IMDb synopsis:
John Quincy Archibald's son Michael collapses while playing baseball as a result of heart failure. John rushes Michael to a hospital emergency room where he is informed that Michael's only hope is a transplant. Unfortunately, John's insurance won't cover his son's transplant. Out of options, John Q. takes the emergency room staff and patients hostage until hospital doctors agree to do the transplant.
Here's another:
Desperate Measures (1998)
starring Michael Keaton, Andy Garcia, Brian Cox, Marcia Gay Harden, Joseph Cross
IMDb synopsis:
San Francisco police officer Frank Connor is in a frantic search for a compatible bone marrow donor for his gravely ill son. There's only one catch the potential donor is convicted multiple murderer Peter McCabe who sees a trip to the hospital as the perfect opportunity to get what he wants most freedom. With McCabe's escape, the entire hospital becomes a battleground and Connor must pursue and, ironically, protect the deadly fugitive who is his son's only hope for survival.
Here's a third one, but it doesn't involve a sick child:
Deliver Them from Evil: The Taking of Alta View (1992 TV movie)
IMDb synopsis:
Rick Worthington assaults Alta Vista Hospital, taking four women, a man and two babies as hostages. He wants to kill Dr. Garrick, who, according to Worthington, ruined his life by sterilizing his wife. He threatens to detonate a bomb.
For another hospital hostage (no child)...
The Hostage Heart (1977 TV movie)
starring Sharon Acker, George DiCenzo, Cameron Mitchell, Peter Palmer, Belinda Montgomery, Carl Weathers, Bradford Dillman, Loretta Swit, Vic Morrow, Hari Rhodes
IMDb synopsis:
When a billionaire industrialist goes into a hospital for a heart operation, some people who claim to be revolutionaries enter the operating room and draw guns and holds the man and the entire surgical staff hostage. They then demand $10 million. The administrator calls the police and the FBI. The police claim jurisdiction over the matter, and the man in charge is intent on taking them, even if some of the hostages get killed. Eventually, they learn that some of the people in hospital are with them.
Those might make an interesting marathon!