We have been in similar situation since DD was 10 months old, for months I couldn't work out what was causing her lengthy NWs ( they weren't every night but up to 50% of the time) and we too gave her meds thinking it was teething related.And went to the Dr only to be told it was 'sleep hygiene' issue.
But I just couldn't understand- and still can't- why she couldn't go back to sleep for 2-4 hrs.
In the end I figured it out- its always down to OT. We still get long NWs but not as frequently.
So may be its the same in your case? We came close to turning to a sleep training specialist too. Things you do to try make them sleep better
but yes, OT is what's been causing night chaos here,I know too well about having to go to work on no sleep and surviving rather than enjoying the day