Iris unguicularis blooms during the winter, and Iris lazica is a little later (Feb-March for me). The white one you're looking for might be Iris albicans, but I don't know who carries it.

I have a feeling it might be better sought as a pass-a-long plant, although you might get lucky and find it for sale. I got my white-flowering one, and the purple one that flowers at about the same time, as gifts from fellow gardeners. If you get to any of the plant swaps, you could ask for someone to bring some for you.

I think it also depends a little on the micro-climate as to the date of flowering - there were both white and purple ones flowered and gone by the time mine flowered - and the lady who gave me mine had had hers open for a week or more, but hers are in a sheltered area, facing south, under 40-year-old crape myrtles.

There are vendors who carry Iris albicans.

Here is a link that may be useful: Historic iris vendors