Thingy has a range of calls, including a whimper. She doesn't do that one often and so far it's never been when she's been really distressed. Generally she does it when she's pretending to be Orphan Annie. You know the sort of thing: "I'm a poor little orphan and nobody feeds me..." She tends to save it for gullible strangers.
She does hate being in her cat box and whines all the way to the vet, in spite of all my reassurances and my putting a few pellets of food in the box's food tray, but she's fine as soon as I let her out (she loves the vet because it's a man!). I put that down to nothing more than irritation.
The one time she has been in really distressed was when she'd not long been with me and her hind legs gave way when she was getting out of the litter tray. She couldn't stand on her hind quarters but the cry she gave was more of panic. That's when she got taken to the vet - I was really frightened for her. But it turned out to be hyperthyroidism and she's fine now she's on daily medication.
You're doing the right thing, in my opinion, if you are at all concerned. The vet will provide you either with reassurance or a solution.