Does this camera happen to be the Nikon D800? It's not quite consistent with the common 'oil/dust spots' as can be seen here, yours are more squiggly. But these have (as to my knowledge is Australia) have a warranty fix for it.
The repair centre may be right, however it's important when they told you. If it was:
- When you gave it to them and gave them image examples
and the straight away said it's under a layer and can't be fixed (AND didn't charge you), then that's fair enough. If;
- They attempted to repair it, without image examples
and they told you after and still charged you, this is wear they have a leg to stand on. You should still get a refund. If;
- They repaired it, charged you and gave you no information at all
and you found out when you went to take some shots after you got it back, then that's a definite refund.
What it true is that image sensors do have layers. They also have filters, generally made out of glass and are IR stop types. Depending on the model, it's highly likely that you can (very carefully) remove the filter and clean underneath it. In some cases, the filter is just replaced because it's easier than to clean.
In the very, very rare case that it's actually caught inside the CCD or CMOS layers, then the image sensor needs replacing and can't be cleaned. Concluding from the inconsistencies from your two images, this is not the case.
Again, this could be a certain model where the filter can't be removed.
It's not a stuck or dead pixel.
If the camera is only two months old, take it back to the manufacturer. You shouldn't be paying for any of this to be fixed.