I went through the exact same thing with my LO now 18months, for about a month and a half solidly....early wakings and then longer NW - it was indeed teeth and once they'd cut through and she was all well again she went back to sleeping til about 6.30/7am. I think you're LO is doing ok though TBH
As for a 5.30 start I had a year and a bit of those....in the end, once I had totally ruled out teething (as this did play a big part) I just left her in her cot each morning for longer. But I think it's something she just grew into after a while. She woke at 5.30am, and I left her until about 6.15am. Think after that she just put herself back to sleep or plays quietly for half an hour or so. I dooo so know how hard a EW is, I hated them for ages and had them for ages.