I have had thyroid surgery (twice) and I didn't have this problem immediately after surgery.
It could be many things. Intubation, indeed, can cause a big problem. Some people can actually get scar tissue from the tube.
She could also be forming scar tissue in her neck from the thyroid surgery that is now pressing on other structures in her neck. With time, that could go away.
Another thing to consider is that when they do pass the tube down your throat they irriate all the structures in that area--vocal chords, bronchial area, etc. Couple that with naturally occur post nasal drip from seasonal allergies and "that" area can't handle it as well.
I am going through something similar. We aren't 100% sure, but back in April my doctor and I suspect that I contracted Whooping Cough (no one suspected it at the time, but now that the cough went on for 3 months, they do--plus the massive increase in cases of it here gives them a bit of a clue??). Anyway, even though my cough (5 months later) is gone, any little bit of post nasal drip gets my throat tickling and gets me choking. Now, I've always had some post nasal drip but I never really noticed it nor did it bother me enough to take anything. Now, I clear my throat all the time. I am told that whooping cough strips the bronchial area and you're "not the same" for quite some time. I think this can go on with the breathing tube issue after surgery. It maybe just made her vulnerable in that area and now she is sensitive to any mucous.
I will say that about 9 months after my thyroid surgery, I felt like I had that "lump in the throat" feeling when I swallowed but on the left side of my throat. I ended up going to an ENT who check out my vocal chords and stuff (I was scared I was having a cancer regrowth). Everything was fine and he said the sensation was probably due to mucous or GERD.
I don't know if my ramblings help! Just trying to give you some ideas on what it could be. If it doesn't disappear in a few more weeks, really, the best person to consult is an ENT who can take a look at those structures right in their office.