I'm happy to help! :-)
Yes, cold tail causes pain and shaking around the anal area - it is the base of the tail where it attaches to the body that is painful, so dogs hold the tail clamped to their body.
The other thing I had wondered about was an anal gland impaction, but the history of having a bath and this starting after that is just so suggestive of cold tail.
I can tell you a bit more about anal sac issues. Not all dogs "scoot" their anal area when this happens.
The anal sacs (or anal glands) are little glands located at the 4 o'clock and 8 o'clock position if you are standing behind your dog. They are normally about the size of a chickpea. They have a little tube leading from the anal sac to the anal opening, and what Mother Nature intended was that every time your dog defecates, a few drops of the fluid contained in these sacs gets deposited on the feces.
Sometimes, however, the little tube gets blocked and the anal sac cannot empty. Anal sac fluid is continuously produced by the body so the sac gets more and more full. Eventually it can rupture out through the skin.
With anal sac issues, the dog does not usually hold the tail clamped down, and people usually notice some swelling BESIDE the anus.
Here are some links to further information:
So, although anal sac problems are still possible, I do think this sounds more like cold tail. The only way to really know would be to do a physical exam of course. But these would be the things that I would be considering!
I do hope that helps you to help your dog!