Could the wood shavings I put in my rabbits cage be causing her the sniffles and watery eyes?

1) Yes. 2) Take her to the vet. Sniffles in the rabbits can be deadly.

Yes, it's possible. Aspen is the only safe type of wood shavings. But that doesn't mean the shavings are absolutely the cause.

Dental issues can also cause runny nose and eyes.

I find that wood shavings or any loose bedding just makes an unnecessary mess and makes more work for you. There are easy (and cheaper) ways to set up a cage. Is your rabbit litter trained? They train easily. If you'd like to see some alternative (and much easier) ways to house your rabbit, take a look at the following website:
http://rabbitsindoors.weebly.com

(It is my website)

Absolutely. The only SAFE wood shaving for small pets is Aspen, and even that can be dusty (which can cause respiratory issues.) Pine and Cedar both contain phenols that are TOXIC and ABRASIVE.

One of the few wood products suitablee for bedding is aspen. Anything dusty can cause sniffles or sneezing.
You might switch to a paper product for bedding and see if that helps. A lot of times, eye infections are the result of splinters in the eyes.

Yes woodshavings is could be the cause but there are many of other reasons your rabbit has the sniffles and watery eyes - I would advise a trip to the vets. I know lots of people are suggesting aspen, but if your rabbit is inside may I suggest fleece. I have kept my rabbit on fleece for many years, as long as the fleece is safe for pets and you do not wash it with laundry detergent it is safe. I would advise cutting your pets nails if you are going to do this though as their nails could easily get caught in loose threads. Apart from that the fleece doesn't have any dust which can cause respiratory problems and its actually rather warm. I'm not sure I would suggest this for outside because in summer it can be too hot and in winter I don't think it would keep them warm enough. My rabbits love the fleece I see them sleeping more on the fleece than in their hay. Also you maybe thinking but they will poop all over the fleece. Not if you litter train your rabbit! My rabbits have a cat litter tray which I use back 2 nature and the tray means they have more space than a rabbit litter tray and the back 2 nature bedding is nice and easy to chuck away when the litter is ready to be binned. Also I put towels on the floor then the fleece on top just in case they do accidentally urinate but I found they don't do that anymore. Anyway good luck with your rabbit and please take them to the vets to make sure they are 100% okay!!

Try a different kind. See if s/he improves.