The MRI on Friday showed no evidence of a tendon tear or swelling, and the injury is being treated as overuse syndrome, the team said.
"It's gotten mildly worse, but it's not terrible," Hill said Saturday. "I'll treat it day by day, and they just want to make sure that moving forward we're not pushing through something that should be stopped."
Nationals manager Manny Acta said Hill will seek a second opinion Sunday at Duke University.
"I feel bad for the kid," Acta said. "For the last five years he hasn't been able to pitch a full season in the big leagues or the minor leagues."
Hill missed the entire 2005 season after undergoing Tommy John surgery.
Last season, he had surgery on his left (non-throwing) shoulder, which had caused him to change his mechanics, resulting in right elbow problems.
"It started about a month ago as I was gearing up, starting to break off curveballs and bullpens before spring training started," Hill said. "We've been treating it ever since, so it's just one of those things that it hasn't gone away, so that's why we're trying to address it."
Hill is slated to start Wednesday against St. Louis in Jupiter.