I vacuum away cobwebs, ants & any other small insects I find while cleaning the house. My intention is to clean the house but I still feel bad about those insects. And most of the time I don't clean the vacuum cleaner bag on the same day & even if I do so some insects are already dead. I'm unable to use brooms or anything to clean the cobwebs due to medical conditions. Is it a sin to do so?
Buddhism doesn’t deal with sins, it deals with consequences of our actions (karma).
Your example seems like a trade off between feeling bad for the insects on one hand, and having a dirty home on the other. The former, being merciful towards other living beings (karuna) is considered a virtue in Buddhism as it can save us from feeling bad.
Sometimes life is about choosing the option giving us the least bad consequences for everyone involved, out of all the options. The effort to balance our actions (upekkha) is considered yet another virtue in Buddhism as it unifies others wellbeing with our own, saving us from destructive self-sacrifice on one hand and selfishness on the other.