I have been doing low carb for 5 years. You need to remember that your body does still function correctly at times. I spent my first year of low carb with low blood sugars, but at times, I would have very high blood sugars. Your body will try to produce glucose if your blood sugar gets low, and Insulin if they get high. Your meds are also doing this job too, so your blood sugars are going to be all over the place. You are manipulating your blood sugar by eating less foods that spike blood sugars, and still taking meds that also lower your blood sugars.
It took me 1 year to get off meds, after figuring how to keep BG below 120 mg/dl. After getting off the meds, I stay in the 80-110 range ( for 4 years ) without a lot of work. Medicine complicates things.
Also, I would suggest you post a menu for the day, many times we think we are doing low carb, but are eating foods that spike our BG. Especially LC products, and sugar alcohols, but also SF foods, and diet pop.
Use your meter, and when you get a spike in BG, look at the ingredients of the meal you ate before. Something in that meal spiked your BG, and you shouldn't be eating that.