Hi and welcome to the forum. What are your BG levels before and after a run? If they are ok, I don't think you would need to test during a run. But if you are worried, just take your test kit and do one or more tests so you have peace of mind.
I don't think there's any reason you can't keep running as much as you want to with T2.
I'm assuming you are not overweight, in fact are you quite lean? If so, you might have another type of diabetes - there are more than 2 types. About 20% of T2s are not overweight. Many of those probably have another type, but don't know about it. If your BGs haven't come down to a safe level yet, let me know and I will post some links for you. What sort of food are you eating?