Yes, this does happen. I have had 2 full massages in my life - no scented oils, just the same almond oil I use myself - and an experienced masseuse - and felt just the same.
My physiotherapist (very experienced) has come across a few people like this, and has a hypothesis that it happens mostly to those of us with inflammatory conditions (fits with the comments above).
I personally don't find it makes me feel better at all, so never book one. Having said that, very limited massage, just on the affected limb (or part of the back) does help.
I hesitate to suggest this, as it is completely unproven, but we have wondered if there is a connection between the inflammatory condition and release of some chemicals into the body that makes me feel unwell. That would be why a full body massage has a deleterious effect, but having a limited one feels more beneficial.
On this rather shaky hypothesis, I wonder Leonora, if it is worth suggesting to your masseuse that she limits the massage to the worst bit and see if it helps? Apologies if you've already tried that.