You could check your cells under the microscope and compare the scatter pattern in FACS with freshly fixed cells.

I would not freeze them, put them at 4 degrees

Even though they are fixed, your cells won't cryopreserve well. Try adding 10% DMSO to your buffer to prevent damage or use 10% DMSO in FBS to store your cells (PMID:27798817).

You can keep fixed cells in FACS buffer at 4°C for few days.