Thanks, I often have trouble on the English side with onomatopoeias. Sigh is definitely wrong, you're right. Sniffle is closer, but still not quite right; ひっく is a spasm of the respiratory muscles (which is why it breaks up her speech), not a repeated sniffing. The perfect match is "hic"; I'm not sure why I didn't use it at first... maybe I was afraid of people thinking she was drunk?
I'm bac... uu... hic!Eh!?I got bullied by some kids from my cla-... hicBullying is not coolHey! What's the matter, Subaru!How dare they bully my cute Subaru...Absolutely unforgivable!I'm going out for a bit.Wait, Gin!