Thank you very much for sharing!! I’ve been concerned about damaging excellent sleep habits in the long run, but he’s definitely going through it and needs comfort. I like your approach!
Loki sometimes gets like that, especially since he was neutered. He’ll stand in front of the counter where his treats are and stare at them. If I walk by, he’ll plop his butt down in front of the counter and stare at me, silently protesting and making his demand.
I’ve learned that the most effective strategy for dealing with this (other than providing sufficient toys, exercise, and entertainment) is to tell him “no” and stick to it. You can still be consistent in giving treats for tasks and behaviors you normally reward, without giving in to plain demands for treats. If you give in once, they’ll continue to push until you stop; consistency in reward circumstances is key. Just because you say “no,” it doesn’t mean she’ll hate you for it—though it can seem that way during the adjustment period, lol! Giving carrots when she is making such demands is likely perceived as giving in; it’s better to give them to her when she is calm and not demanding things from you, reinforcing the behavior you want.
My nickname for my husband when we’re eating is “the weakest link” 
. He usually ends up with both the little beggars drooling one foot away from his plate because they know I’m not going to cave, but they know he probably will.
In humans, there is a type of dementia characterized by food cravings. I’m wondering whether there’s any canine cognitive dysfunction going on.
In any case, given the coughing and head shaking, I’d recommend a vet check.
I agree with Brandy that a visit to the veterinarian would be far superior to self-diagnosis. At her age, she may want assistance!
Third vote for a comprehensive veterinarian examination, including geriatric bloodwork and a thorough thyroid panel. When a dog suddenly exhibits new, unusual habits, the first thing to do is rule out any medical causes - this is especially important when the dog in question is a senior! With such a wide spectrum of symptoms, a variety of problems could be present. I doubt she’s just doing those things because she’s “stubborn,” and I hope you and your vet can get to the bottom of it and help her feel well soon.
Chiming in to highly advise you to have her checked out by a veterinarian. This is quite crucial. A senior dog that begins to exhibit unusual behavior should always be taken in for a thorough examination and blood work to determine how things are operating. While this could be the result of canine dementia, you don’t know, so the first step is to rule out any medical conditions the dog may have.