It is good news that things have started moving but keep going with tempting her with different stuff. Try grating the carrot too. It is sweet, as is apple but anything to tempt her at the moment and she is not eating loads. If she is chomping at the syringe this is a good sign as she is taking it willingly. Tickle / gently stroke her under the chin with her parsely, this sometimes works they snatch it from you.
If you'd have told me this 2 weeks ago I would have no way done it for fear of having my fingers bitten off! But now she's spayed (I keep forgetting, yet the spay, according to the vet, caused all of this) I'll try that I don't want to annoy her though,because when I went through my operations I was very sore and in pain, heavily dosed up on morphine and the LAST thing I would want is someone waving mcdonalds under my chin I'll try that though