Hi, it's perfectly normal for bg to soar during an illness - even if you are not eating. The body releases stores of glucose to fuel itself in the fight against it, so the bg will not be related to your carb intake or activity.
But three months is a long time. It might be worth checking that you are actually free of the virus and if you are, maybe this is the new normal and you need to, with the assistance of your health care team, rebalance your basal and carb/short action ratio.
After all, it's not unknown for diabetes to be triggered by an illness - so it's possible that it could worsen as it were if you are ill, particularly if you had been making a small amount of insulin yourself, which is a possibility if you were on low doses, and that's now reduced or stopped.