How do I find and eliminate a sickly sweet smell in my apartment with no obvious source?
Unfortunately nothing seems to work. I have tried an UV light, but no anomalous things popped out. I did not try an IR camera, and that's due to costs. The solution: move within the month. At this point it is the most economical. I have about a week left before I renew my lease, so unless something miraculous happens during that time I'll just rent a truck and find a new place.

Update: It's a been a long time since I posted this and have moved around quite a bit. I am pretty sure now that the smell was some form of smoked drug, like meth or crack, seeping in from a neighbor. I arrived at this conclusion after encountering a severely impaired individual on the train who smelled the same way... coincidence perhaps, but it fits the pattern