Are you sure that you actually got the 6.5x55 swedish round or did you get another 6.5? You said it fit loosely so this might not be a possibility.

264in (6.6mm) and up
Name Bullet Length Rim Base Shoulder Neck OAL
6.5 x 50 SR Arisaka 6.705 (.264) 50.39 (1.984) 11.84 (.466) 11.35 (.447) 10.59 (.417) 7.34 (.289) -
6.5x55 mm Krag
6.5x55 Swedish 6.7 (.264) 54.864 (2.16) 12.192 (.480) 12.17 (.479) 10.688 (.420) 7.468 (.294) 80.010 (3.15)
6.5 x 68 6.70 (.264) 75.02 (2.956) 13.00 (.512) 13.30 (.524) 12.18 (.480) 7.60 (.299) 86.50 (3.408)
6.5-284 6.70 (.264) (2.170) (.473) (.500) (.475) (.295) (3.110)
.260 Remington 6.70 (.264) 51.7 (2.035) 12.0 (.473) 11.9 (.470) 11.5 (.454) 7.5 (.297) 71 (2.8)
6.5 mm Creedmoor 6.70 (.264) 48.8 (1.924) 12.01 (.473) 11.9 (.470) 11.7 (.459) 7.54 (.297) 71.6 (2.82)
6.5x47mm Lapua 6.70 (.264) 47 (1.9) 12.01 (.473) 11.95 (.470) 11.53 (.454) 7.41 (.292) -
6.5 mm Grendel 6.70 (.264) 38.7 (1.524) 11.2 (.441) 11.14 (.439) 10.87 (.428) 7.44 (.293) 57.5 (2.264)
.264 Win Magnum 6.70 (.264) 64 (2.5) 13.5 (.532) 13.1 (.515) 12.5 (.491) 7.6 (.299) 85 (3.34)
6.5 x 52 mm Carcano 6.807 (.268) 52.50 (2.067) 11.42 (.450) 11.42 (.45) 10.85 (.427) 7.52 (.296) -

Take a picture of it, the lugs on the barrel, and the feed ramp and I might be able to tell you if it has been and to what caliber it was changed. There should be a name on the barrel/serial number if it was converted and i might be able to look it up that way as well.