Well, in my opinion, both your examples are acceptable in English:
I not only lost all my money - I also lost my passport.
I did not only lose my money - I also lost my passport.
The latter example with "did+lose" simply seems more emphatic though I'd suggest the following variation might be more common:
I didn't just lose [all] my money - I lost my passport too!
What do you mean by "old English"? I hope not "Old English," the ancestor of modern English. Old English is an entirely separate language from modern English. It's like comparing Late Latin to Portuguese.
So perhaps you meant old-fashioned English?
All of the examples above are in perfectly acceptable modern English.
Student or Learner