I'm guessing you live in a condo.
The neighbor above me was renovating his bathroom, and suddenly water came down to my bathroom through the vent opening.
Why? In other words, what was the source of the water? What was the cause of the deluge? The answers to that are critical in determining if the neighbor owes you anything. If he was doing the renovation personally and screwed something up he would be liable. If a contractor was working in the bathroom and screwed something up then the contractor would be liable and you would have to deal with the contractor and the contractor's liability insurance.
I had to through away all towels and toiletries and sanitize my bathroom.
You have some documentation of that? Of your costs? You'll need that to get any money from the responsible party.
The neighbor's insurance called and I explained the situation and asked for somebody to come and look at the ceiling but they insisted that it is my sole responsibility to find out if there is any damage and send them photographs...etc. at my own expense. This means if I remove the "drywall ceiling and find no damage, I have to pay for removal and replacement!
Since you actually had some damage to some items and if you incurred cost to replace them, your own insurance could cover the cost of those items and the cost of removing and replacing the drywall and repainting the ceiling. Then your insurance company would seek recovery from whoever caused the damage.
If you don't want to make the claim on your own insurance or your deductible is higher than your costs then, yes, you will have to incur the cost of opening up the ceiling for inspection and restoring it afterward if there's no damage. If you decide you want to open up the ceiling make sure you have somebody make a video of the process and any damage that you find.