As I experienced problems a bit similar to yours, you might be interested in this thread:
I agree with Matt that you are probably fine now if you have cancelled the subscription in the new app.
However, whatever you do, don’t subscribe again in the new app! That’s why you have been billed by Apple. Instead, let the current (cancelled) subscription run out and then it could be fine. If not, try solving the issue without starting a new subscription. If your subscription doesn’t carry over from the old app, try what I did in the thread I linked, ask here for advice but don’t buy it again from Apple.