What should I do about slight human errors in my data?

Congratulations on finishing your thesis, and I'm sorry to hear about the stress and lack of sleep. Try not to be so hard on yourself. Think about the cell count mismatch as measurement variability. I doubt anyone could have gotten a perfect count. Humans make mistakes and that is to be expected. That said, it's good to take this seriously and check that the research findings are not sensitive to that variability. Be assured that this kind of situation is fairly common, especially with manual, tedious analysis like hand-counting cells. If you redo it later and the numbers don't match exactly, that's not surprising. The important question is whether the scientific conclusion changes. In your case, it sounds like it doesn't: the trend is the same and the p-values are essentially unchanged.

Since the conclusions didn't change, I would not panic or lose sleep over this. If you still have time and access to the data, the cleanest thing to do would be:

1. redo the counts carefully (or have someone else independently count a subset),
2. update the numbers if they shift slightly, and
3. document the procedure clearly in your protocol. But I would not go down a rabbit hole trying to reconcile every single discrepancy from months ago. Manual counting is not perfectly reproducible at the single-cell level.

On your other question: yes, it is normal that your advisor did not check raw data at that level of detail. Advisors check that things look plausible and reasonable, and often focus more on the research questions and writing quality. In most fields, it is the student's responsibility to double check the data quality.

The fact that you went back, noticed it, and are thinking carefully about it is exactly what a good researcher does. If the conclusions stand, you did your job. I would recommend documenting somewhere for the sake of future readers that the cell counts don't quite match what's in the data, including the correct counts, and showing that this didn't change the findings. That could be an erratum, or a note in a preprint version online (e.g., bioRxiv), or as part of a supplement to the thesis if it can be added.

Are you within the measurement error of this kind of experiment?

Every measurement, every experimental data, is "wrong". Nothing is perfect. So one has, best before you start with experiments, think about what kind of deviation is reasonable. The recount is 502 instead of 499 ? Well thats probably within the expected range. That means for experimental science, they are the "same" value. The count is 10 instead of 15? Off by a third, that doesn't sound right.

Getting the exact same values is often the start of how fraud is detected in publications. You never measure exactly the same data twice. That does not mean that one of that measurements is wrong, it just means that every real world data taking has a finite accuracy.

So my advice: Get a feeling for how big your deviations are (percentage puts it in perspective) and get an idea of how much of a deviation can be expected.

I would not expect your advisor or anyone else to check the entirety of your work. It would be good to do some validation on a subset to get an idea of reliability (both your own counts and inter-rater), but if you've already submitted your thesis and didn't do this, I would not worry at all. However, some things your advisor probably should have been aware of and should have trained you on/prepared you for might be:

1. Error is normal in manual cell counts, I would not blink at discrepancies of 5-10%, worse discrepancies may occur when the task is more difficult (for example, if you're counting something difficult like morphology).

2. Automated methods are also going to have some intrinsic error rate; even if they're able to give you exactly the same count with the same images, that just means they're making the same errors repeatedly.

3. The more important thing to concern yourself with is not measurement error but measurement bias. An example source of bias would be if you started with your control samples, and then your test samples. Or if you always start your day with a control sample and then do a test sample. Your counts might change either as you become more of an expert at the task or as you tire of it. Much better to randomize the order.

If you've gotten different counts but the same statistical result, then nothing has meaningfully changed.

I want to reinforce what other answers have said more or less directly: Counting is a measurement, and every measurement has an associated uncertainty. This is a fact of science and not a moral failing; please do not be ashamed.

In many counting measurements, the uncertainty is effectively zero, so we often ignore it. Your case is clearly one for which the counting uncertainty is nonzero. Whether this uncertainty is significant seems to have been indirectly determined as "no" by the fact that your statistics remain unchanged with the second count. But if you wanted to be most thorough, you could incorporate the counting uncertainty explicitly into your analysis. You have two data points, so you can estimate a variance.