Just think how you'd do it for, say...a western blot. You'd have all your densitometry for your protein of interest, all your densitometry for your loading control, and you'd...divide the former by the latter to get your per-sample protein expression. Then you'd look at your (now normalized) protein levels and see if anything interesting is happening.

You would never work out the SEM of your loading control and the SEM of your GOI and then...do stuff with those SEMs: that's madness. You normalize each sample first, THEN do your comparisons.

qPCR is no different: you take exactly the same approach and do exactly the same thing, with the exception that qPCR data is in log-space, so divisions become subtractions.

So: let's say you have five samples of treated cells, and five control samples.

Isolate RNA, spec it, QC it, make cDNA.

Now, run qPCR, using these ten samples, in triplicate (so three wells per gene, per sample) for two (or three) validated reference genes and your GOI.

This will give you replicate Cq values for everything.

First thing: manual QC.

Look at the replicate Cq values for each sample, and see if they agree. This is basically "did you pipette the same way three times, and also did anything weird happen": you might see something like 22.2, 21.9, 22.1 as replicate Cq values for GAPDH, and this is great. The final GAPDH Cq for that sample is the arithmetic average of those three Cqs.

If instead you have 22.2, 21.9, 26.8, then you can pretty safely assume well #3 just went weird, and discard that data. Use the mean of the two remaining (non-weird) Cqs.

So eventually you should have, for each sample, mean Cq values for your GOI, and mean Cq values for each reference.

Make your two reference gene Cqs into a "normalisation factor": the average of the two.

Then subtract this from your GOI Cq for that sample. This is the dCt value for that sample, for that GOI: that sample is now normalized.

Do this for all your samples. Now all your data is normalized, and is in the form of dCt values.

Note that dCt is somewhat counter-intuitive, as low numbers are high expression, and vice versa. You can just multiply everything by -1, because the statistical comparisons are exactly the same. "-dCt" is a perfectly valid metric.

dCt values are approximately normally distributed, and entirely statistically-tractable. Use these for your stats. From the example above, you will have, for your GOI, five treated dCt values, and five control dCt values: this can be a straight T-test. If paired data, paired T-test.

There are other ways to do this that are mathematically identical but less "OMG LOG SPACE SCARY", which I typically use because log space scares me, but this basic method works and is easy to work through.

So, TL:DR, ignore SEMs, they're not useful here. Go back to the raw data.

If you have data you're willing to share, I could workshop up a basic spreadsheet for you.