Convenia will not affect Squeak's BG readings. The reason we suggest not giving it, is because it is a long acting antibiotic and once it's in your cat, you can't take it back out. If your cat had an adverse reaction to it, then it could be a problem. Convenia can persist in the body for up to 65 days. It's meant to treat bacterial skin infections but sounds like your vet used it off label.
Some side effects are vomiting, diarrhea, decreased appetite, anorexia, lethargy.
Since my Wink has adverse side effects with many antibiotics, I want one that can be stopped at any time if he has bad side effects.