if you're having bad lows, then you need to further reduce your insulin dosing. Try reducing by say 10% and then if that is not enough reduce by a further 10%.
Are you using basal-bolus regime, with separate long and short acting insulin? If you are you can look up how to do basal testing. This will help you set your long acting insulin to optimal level.
An alterative approach to sliding scale is to dose fast acting insulin based on carb counting. You dose insulin in anticipation of how many grams of carbs you will eat.
Are you eating low carb as well?
Test frequently while you work out what your adjustments are.
I experienced the same problem and I just started snacking a little more and it worked. Also checking my blood sugars more often and making sure I'm not over correcting when I eat.
I wouldn't edit your insulin dosages manually without consulting your doctor/endocrinologist. But in the meantime eating small amounts of meat or PB, or even possibly popping a few small hard candies in your mouth can round out your blood sugar slowly and hold it constant, which may result in less low blood sugar values.
It is also entirely possible that the new medication you were prescribed is just taking effect on your body and your body needs to get used to a different medication. From my experience, when I switched medication, even if it was just a different brand of insulin, my body went out of whack for a week or two until it got used to it.