You certainly can take pictures. And not to be too reductive: cells are visible in a light microscope. The point is that the scale that cells are at is not really at the quantum level. People have been interacting with individual cells for decades: https://www.youtube.com/watch?v=GTiKFCkPaUE
I also have a degree in physics but in addition I have a degree in computer science. 36 Trillion is not a very large number for modern computers anymore. I am sure even today we could build machines that would filter the cells in your blood by images and do it at 10s of millions per second.