Hi and welcome!
Good that you have booked her in! Coughing and sneezing without any other symptoms are generally not to worry about, but once you get any raspy, crackly or wheezing breathing with them, you need to see a vet promptly to make sure that the airways and lungs are not impacted. There are some nasties around that can hit out of the blue and progress very quickly.
Coughing after eating can stem from too greedy eating and sneezing without any further symptoms is usually caused by hay dust. Unlike a human viral cold, a bacterial URI doesn't generally start with sneezing and coughing, but typically with breathing issues that come from deeper in the airways.
I haven't noticed any breathing problems from wood shavings which I used in the olden days before I switched to fleece a decade ago, but sensitivity to hay dust and pollen is far more common. Working out what is causing an environmental vector respiratory issue is usually a process of trial and error by looking at all the possible factors in turn. Personally I would always start with hay rather than bedding.
Like with greedy eating coughing, something gone down the wrong way or stuck can cause a coughing fit. Any regular or persistent coughing should be seen by a vet; the same as any sneezing if it is not a nose clearing one-off sneezing fit or piggy wash nose clearing sneezing a few times a day.
You have done absolutely the right thing! I hope that you are catching whatever it is early on.
Your vet is very likely to treat for a respiratory if there is the least hint, simply because they can be fatal or permanently damaging if left untreated.