If you can stand almost anywhere in the room (except maybe next to the curtains) and clap sharply and hear the ringing, it is flutter echo. Caused by parallel walls and not enough absorption at mid/high frequencies.
If that's the case, you can either DIY some absorption panels, or buy some Markertek or Auralex studiofoam and apply it to the walls.
Auralex has a good primer on acoustic treatment at
www.acoustics101.com - check it out.
When you say "recording room", I'm assuming you mean the room where things are when they get recorded, NOT the room all the recording gear is in. These are typically called "tracking" and "control" rooms, respectively.
A tracking room doesn't have to be symmetrical - you can alternate foam and bare walls, generally putting foam on one wall and bare on its mirror counterpart. This means where there is foam on one wall, it's not on the opposite wall, and vice versa.
Sometimes heavy curtains or moving blankets hung 3-4 inches off the walls is enough.
If your floors are bare, the flutter echo can also come from floor/ceiling parallelism. Foam on the ceiling will fix this.
Try moving the instrument (sound source AND mic) around in the room, making test recordings. That may help. In some cases, draping moving pads around the sound source and mic (not between the two) can help tame room anomalies.
C'mon back if none of this helped - don't forget the hand clapping experiment so we will know if this is the problem... Steve