Unfortuantely, I'm going to have to step away from my computer to help a neighbor who has some health issues but I wanted to provide a response for you and list the various reasons why a female who's just delivered puppies might pant....some perhaps more serious than others.
1. She could still have an undelivered pup which isn't likely to be viable. If you know for sure that she had three puppies to deliver, then this reason can be crossed off the list.
2. She could be running a low grade fever which is commonly seen after whelping for about 24-38 hours or a little longer; this is normal for some females. If you have a rectal thermometer, you can take her temperature. Normal is between 100 and 102.5.
3. She could be in the early stages of a uterine infection or metritis. The signs associated with this condition might include a foul-smelling brownish or reddish brown vaginal discharge, anorexia, lethargy, fever, decreased interest in the pups.
These dogs will need antibiotics for the problem to resolve.
4. Low calcium which is usually seen after small breeds have been nursing for a while (not just two days) but it's still possible. Supplementation with Calcium Tablets (available at most pet or grain stores) may be something to consider. You can give her Tums if you can't get to the store right away which may provide some benefit. The dose is somewhat empiric but 1-2 tablets are what I'd give.
5. Less likely, but still possible would be a retained placenta. This is actually a fairly uncommonly seen problem but I'll include it to be complete.
If this were my dog, I would take her temperature but wouldn't get too excited if it's high but < 104 degrees.
I would monitor the color and smell of the discharge she's likely producing. If it smells, then she should be seen by a vet pretty quickly.
I would supplement her with Calcium since nursing could create Eclampsia.
But if she's otherwise eating and taking care of her babies, then I might give it another day to determine if the panting disappears...which it most likely will. If it doesn't, then a vet visit may be prudent.
I hope this helps although, again, my apologies for having to log off before you had a chance to respond back. Deb