Hello
@keysys Welcome to the forum. It's normal for blood sugar to rise when we're ill, including with an infection. If you have been on steroids for your chest infection, they also raise your glucose levels while you're taking them and it takes a while for my bloods to go back to normal after I've stopped the steroids (and after being ill without steroids).
When we're ill, we often have to do less/no exercise or other usual activities, which can also raise blood sugar levels.
I've had a lot of chest infections over the years, and my blood sugar rockets, usually before I even feel ill. I think all you can do is ensure you're keeping hydrated, and eating what you can manage (as you are doing).
Are you on a basal/bolus regime for insulin, or just long acting, and have you been given sick day rules in terms of amounts of insulin to take? It's against forum rules to suggest insulin doses, but if you're bloods go too high, you could ring 111 for advice, or contact your surgery.
Sorry you're still feeling weak, and hope you feel better soon. Take care.