You can sometimes tell by the color of the chickens ear lobes but I know that might be hard in your situation.
That's not going to help. Other than the Ameraucana who should be laying blue eggs, every pullet or hen you have could lay a brown egg. There is no genetic link between ear lobe color and egg shell color. Just by luck most purebred brown egg layers have red ear lobes and most white egg layers have white ear lobes, but that is not consistent and it does not give any indication of shade of brown. If you have mixes like the EE, sex links, and golden buffs it means nothing.
Have you noticed the shade of brown changing? A pullet typically lays her darkest eggs just as she starts. Over time the shade of brown tends to lighten. Sometimes you can tell which hen or pullet laid which egg by size, shape, color, or shade, but that isn't always real reliable. On any given day the pullet or hen can have an "oops" where something is different. Still, I've been able to recognize certain eggs sometimes. Depends some on how many are laying.
Typically a pullet starts out laying a pretty small egg, especially if she starts laying at a very young age. It's natures way to protect a small immature pullet from possible damage to her internals by laying an over-sized egg compared to body size. Occasionally a pullet or hen will lay a huge egg, usually a double yolked egg, and almost always without problems, but the more larger eggs they lay the more risk. As the pullet matures the larger the eggs should get. You should have seen this with your others.
If a pullet or hen is laying her vent is going to be moist, soft, and relatively large. A small dry tight vent means she is not laying. It's usually really easy to see the difference once you look. That might help you narrow it down. And if you know which other hens are laying which eggs you can narrow it down further. Hopefully you only have a few to deal with.
I have never used either lipstick or food coloring to see which pullet or hen is laying which egg, just hasn't been that important to me. If I did I'd use food coloring, no way I'd want to explain to my wife why I was putting lipstick on a hen's vent. And I'd not put in in the vent the night before. If someone has done that and the night before worked please correct me, but chickens poop at night. I'd be concerned that they had cleaned the vent by egg laying time.
Good luck however you proceed, it should be a fun experiment. And please report back on your results, whatever they are.