The sudden 'walking sideways' thing could mean she has a balance problem, which could be related to something going on in her ears, perhaps in the middle ear or inner ear.
Are her eyes constantly flickering about? That would also be a sign of something wrong in the inner ear.
As ggreg mentions, it's possible, if there is a middle ear infection that some secretions are coming down the Eustachian Tube into her throat, and that might be the cause of her cough?
In my opinion she needs to see a vet for a proper exam.
MAKE -- I agree with all the above advice, take your dog to a vet!!! He will be able to look in her throat and feel of her neck and do bloodwork, and will be able to rule out her throat or thyroid having a problem. If you will do a search in this section for "dog cough," or words to that effect, you'll find a lot of people have dogs who wretch and cough, so sad.
While my vet thinks it's ordinary allergies, and others have gotten diff reports from their vets, I will always think it's some burrs in our yard that grow with weeds, the mower keeps them down, but I think one gets in his throat now and then and he coughs and coughs, I feel so sorry for him! The vet gives him meds, but when those run out, I give him a little milk with honey 2x-3x a week, and a prednisone tablet (the vet will give you that most likely) or whatever cough meds he prefers, and that will also help.
And each dog I've read about has a little something diff about them that Is part of the problem, like yours moves to the side... which suggests to me anyway, despite my suspicion about the stickers with mine, is perhaps your dog has an ear-ache, and it's dribbling down into her throat, making her cough. If she scratches her ear a lot, could be clearing that up with help.
Food type is also something to look into, a someone else here mentioned. Your dog may prefer smaller chunks of dry food, or prefer wet food, or simply another brand (but switch over slowl if you change food). Hope you get it worked out! GG
She might have something stuck in her throat. Could be a trachea problem. At her age, it could be cardiac or lung related.
You should probably get her checjed at your Vet.
This could be due to many things, but kennel cough and ticks/fleas are certainly possibilities. Considering her age and the danger of these and other conditions, I would get her along to see a vet.
Tony