Only your doctor can advise you on your medication.
As far as rice and wheat goes, both are culprits in raising our blood sugar. While we might be better to avoid them all together they are far too much part of my diet for me to do so. By measuring my blood sugar after a meal I have learn what levels I can tolerate and by having a reasonable amount of meat, fat and vegetables with them the spikes can be smoothed out into an acceptable level. While I am not keen on it I have been told that brown basmati rice is the best for us so that might be worth a try for you.
My best advise would be to get a meter and start self testing if possible (I would have thought as you are on insulin you would be self testing anyway) that way you can find out how much everything effects your blood sugar levels and try and adjust your diet accordingly.