Please tell me, could a broken blood vessel cause swelling in limb?

Yes: Absolutely. The broken vessel will allow leakage of fluids into the space causing swelling , and the body will react to this and you may get more swelling. Apply icepack on/off for 20 minutes for a few hours to help decrease the swelling. If it worsens in size (not color, because it will) then see your Doctor. Also, take an anti-inflammatory such as ibuprofen to help with the swelling. Good Luck.

Of course: The damaged blood vessels bleed beneath the surface of the skin spilling blood into the area surrounding the blood vessel in any part of the body.