Sound like a type 1 diabetic to me.
Avoiding insulin in fear of getting a hypo sounds like a pretty bad idea. Keeping blood sugars at normal range are important to avoid further complications associated with long term high blood sugar. I can only imagen how high your blood sugar must be if you really are a type 1 diabetic and are avoiding to take insulin. That's not healthy at all, if you were diagnosed as type 1, then you should stick to the insulin. Yes hypos are bad and uncomfortable, but long term damage can be so much worse, like neuropathy, glaukoma or even blindness. You can also end up with amputation or stroke. But high blood sugar can easily end with DKA, which usually progress in just a couple of hours. and this condition can be life-threatening and will deffinetly make you end up in the hospital (not only sever hypos leaves you in the hospital, but sever hypers are just as bad). I don't say that all these things will happen to a type 1 diabetic, but if you avoid insulin it's not unlikely that you would get one or more of these complications.
So take your insulin, promises me that. I know hypos can be bad, and be the worst feeling ever, but really 2 times a week aren't too bad. I've heard about people having hypos each day, or even up to 2-3 times a day. I don't know if it makes you feel any better, but I think you've come far in managing your illness when your down to only 2 hypos a week. Trust me it will get easier to manage with more experience, just don't take the easy way out and drop your medications, insulin are important.