It should not matter that you bought at different locations if both are within warranty period. I would definitely send to Canon so both the body and lens are repaired properly. Then when you get the lens back take those screws, remove them, and replace with a very small amount of clear nail polish. That was the trick used in the old days for people that travelled extensively on planes. High frequency vibration tends to loosen small threaded fasteners.
I wonder if the brass mount of even the least expensive Sigma lenses should be considered a plus?