Hi Brittany, if she was my dog I would take her straight to your Vet. Therr could be numerous things wrong with her eye….something in it; an infection; a condition called Entropian where the eyelashes rub on the eye; an ulcer….lots of things. Please don’t risk her eyesight by trying to treat it yourself. Take her to a Vet its the only way you will know whats wrong and have it treated properly.
Good luck!
Puppies, like babies test things with their mouths especially if teething.
You do need to watch her though if she swallowed a peice of wood it could cause all sorts of serious problems. Try and distract her with a toy or a treat…..hopefully she will grow out of it. You could train her not to chew wood too….you’d have to catch her in the act…..calmly and firmly say NO get her to come to you, lots of praise and a treat. Its not too soon for calm sensible training.