It does sound like teething. If she's hasn't got any by almost six months I'd say it was a fair bet. DD had her first at 3.5 months!
To be honest I'm not sure there is a lot you can do to improve sleep when in pain from teething other than to offer some pain relief. I mean, if I had toothache I can't imagine I'd sleep well. What you could do is investigate some more homeopathic options - it's not really something I'm into but others do swear by amber necklaces or Hyland's teething tablets (or similar). But my approach has always been try the 'proper' pain meds for a few nights, then try a night without and see how it goes rather than keeping at them indefinitely.
It's good that she can settle herself independently
it sounds like you know the difference between a protest cry and a 'real' one, but just remember that listening to the cry and responding appropriately is key, not waiting for any set amount of time before deciding whether or not to respond.
Hope the good sleep continues!