Offering and sharing food is a very human, social, inclusive, and caring thing to do, pre-dating our cave-dwelling days. Anthropologists recognize that eating a meal with others (what they call commensality) is one of the most important manifestations of sociality across all cultures. Eating together confirms the sense of belonging to a community. Which is to say, please don’t be angry at people for wanting to share food you may prefer not to eat. They’re just being human.
Of course you can refuse what’s offered — so long as you recognize that on some deep-down level, you risk signalling you don’t want to be part of that person’s community. Instead of risking offending someone, you could accept the cookie but pass it on to someone else, or save it for when you’re running low, or even dump it in the garbage when no one’s looking. (I “lost” a bag of brownies on the subway once. They weren’t very good anyway.) Or you can decline with polite excuses about having just eaten, or saving your appetite for later, or feeling under the weather. A restaurant setting is even easier, since you can usually choose for yourself what and how much to eat.
A non-diabetic friend once pointed out to me that it can be confusing for non-diabetics. For every diabetic who answers, “You know I’m diabetic and can’t eat that,” there’s another (like me!) who answers, “Thank you! Let me just do a quick injection.” She said, “I can’t keep up!”
By the way, your blood sugar will usually rise after you eat even if you don’t eat carbs (or think you’re not eating carbs). A piece of cheese, an egg, a simple green salad can all make blood sugar rise. In both the short run and the long run, your health will be much, much better if you read up on carb counting, and start using your quick-acting insulin. That “needle thing” is your best friend for life.