If your dog isn't showing any improvement after being on the antibiotic for five or more days, call your veterinarian back and let him know so that he can let you know whether he wants to switch meds or give it more time to work. Sometimes, depending on the severity of the infection it is being prescribed to treat, you won't see any changes for 5 to 7 days, so that will have to be your vet's call.
As far as you getting some in your nose and mouth, unless you have a known allergy to cephalexin I wouldn't worry. If you even THINK, however, that you could be having a reaction to it, do as Margot suggested and contact a poison control center immediately. They will be able to advise you on how to handle the situation correctly. Please let us know how you and your dog are.
Ghilly
It is an antibiotic often given for bacterial infections, etc. I would finish the full course given to you unless he gets explosive diarrhea or something. You might try giving him a probiotic or put some Lactinex a blend of Lactobacillus acidophilus and Lactobacillus helveticus. I have used this for years on puppies and adult dogs on antibiotics. You can get it at the pharmacy and just sprinkle some on his food.
Have you tried putting the pills in something like some cheese or lunch meat, peanut butter? I have good luck with the pill pockets. My dog thinks it's a treat.
I've taken Cephalexin myself many times over the years so I don't think I'd worry about ingesting what you did. Maybe the powder inside the capsule has irritated your throat. Try drinking some milk today and plenty of water. Of course, should you feel you are having any reaction like throat swelling, hives, etc, call your doctor. I think if that was going to happen, you would have noticed by now.
We are NOT doctors or Vets here and if you have any concerns, you should contact your doctor, ER or the Poison Control info posted at the top of this forum.
Now, as for the paws...........did this just start and is it all paws? Has he had the problem before? Sounds like there is a good chance he possibly has an allergy.
Try soaking his feet a couple of times a day in Espom salts and warm water
or a mixture of vinegar and water. Make sure you dry the pawn well after the soaking.
Oh, and don't let the dog drink the water. :-)