O's manager Buck Showalter said Flaherty is dealing with a lot of swelling in his glands, although his fever has subsided and the team has ruled out mononucleosis after taking blood work on Wednesday.
"The next 24-48 hours are really key for him," Showalter said. "We'll take it day to day."
Showalter said he was hopeful Flaherty would be able to join Class A Frederick or Double-A Bowie by Monday.
Flaherty, a Rule-5 Draft pick, is hitting .205 with four home runs and 11 RBIs in 60 games this season. His last start was July 23 against Cleveland and he has not appeared in a game since Aug. 1, meaning he would be eligible to return Aug. 17.
With every bullpen arm aside from closer Jim Johnson appearing in Tuesday's 14-inning win, the O's recalled reliever Miguel Socolovich from Triple-A Norfolk to take Flaherty's place on the 25-man roster.
In four appearances spanning two stints in the Majors, Socolovich has pitched seven innings with a 9.00 ERA. He last appeared July 28, allowing one run on two hits with three strikeouts in 2 2/3 innings against the A's.
"It's going to be a day to day thing," Showalter said of Socolovich's tenure with the O's. "We've got to wait and see how it all shakes out."
In 52 innings for Triple-A Norfolk, Socolovich has posted a 1.90 ERA, allowing 33 hits and 14 walks with 52 strikeouts.
The O's also made official the callup of Wednesday starter Steve Johnson. Tommy Hunter was previously scheduled to start on Wednesday, but was scratched after he threw about 30 pitches in the bullpen during Tuesday's 14-inning win.
"We just didn't feel comfortable for Tommy, after getting fully hot last night to come in that game, which he had to do, that it was fair to start the game," Showalter said. "But he is available for an extended outing tonight."
Regardless of whether Hunter pitches on Wednesday, Showalter said he would "probably" start on Sunday in place of Zach Britton, who was optioned to Triple-A after Tuesday's game.
Britton allowed seven runs (four earned) on eight hits and two walks in five-plus innings on Tuesday to push his ERA for the season to 8.10, but Showalter said his option to Triple-A was based more on "convenience" than performance.
"I thought Zach threw the ball better last night," Showalter said. "If that was able to carry him deeper in the game and we were able to play nine innings, he'd probably still be here."
Greg Luca is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.