Lets break this down into 2 sides - the current behaviours of the cat, and your stress.
It can take quite a while for cats to settle to a new home, new routine, new people etc, especially one who has been straying then in a rescue cattery.
Tobias had spent 2 of his 2.5 years as a stray and he gobbled his food like anything, luckily I was still keeping him in his room most of the time so Girlcat could get her food when he wasn't about. But by the time he was fully out & about, after a couple of months, he was much better and within 6 months had realised that food was near enough always there & became a "grazer". If you're at home most of the time then try splitting her feed into many more much smaller feeds, or even just a couple of teaspoons each time then again 10-15 minutes later after the last lot has had time to go down. Over time you can increase the amount & reduce the number.
If your girl had been an "owned" cat for any length of time, she's likely to want to try to bond with you. But she'll be feeling so insecure & clingy that in itself can be worrying, I would see how she is after a while longer. Makes a difference too what the home life is like e.g. just you or others? Are you out at work all day or home with her? When Boycat was PTS I went through weeks & weeks of Girlcat being non-stop clingy & crying, until I introduced her to her new adoring slave/toy boy Tobias. Now she still wants fuss, but now & again rather than being glued to me 24/7.
Now for your anxieties.
You're probably so anxious because you so desperately want this to work, and you've already fallen at least a bit in love with the cat. Her current behaviours are making you think, probably subconsciously, that you are the one failing her as otherwise she wouldn't be so anxious & clingy herself, or have her eating issues.
You may well have PFC syndrome (Precious First Cat), very similar to mothers with PFC (Precious First Child) syndrome. Have a read up on PFC, and you might recognise some of your own thinking & anxieties!
I feel your best course of action would be yes, call CPL and discuss your worries & concerns. But it could be well worth trying to work out a plan of action with them to try to overcome some of the issues you currently have e.g. around the eating, and how to try to reassure her that she is home now.
From the sound of it she's a very sweet cat who just needs a lot of reassurance to overcome a bad time in her life, and if your mental health can be persuaded to cope a bit longer the end result could be oh so rewarding.