Dog Heartworm Treatment

I adopted a puppy from the SPCA last week. He had shots 3 days before I got him, and I took him to my vet the next day, where he had a shot for rabies and was wormed. Since then he has started sneezing, it is mainly clear “snot” which he licks off his nose immediately. He is very playful, and does not have a temperature. I called the vet, they said he could have allergies, but to be sure I would need ot bring him in. I do not want to spend more on another vet visit if I don;t have to. Anyone know if he could just have a cold, or allergies. He has no other symptoms – no coughing, etc. If it is a cold, how long do they last? Any input would be great . I have other dogs and would hate for them all to get sick.

I just got a new kitten last week, and the person I got her from had 4 cats that gave birth. One of their cats kittens would always die, from every litter it ever had, and one of the symptoms that those kittens would get, is they would start getting little bald patches. When my kitten first came home, she was perfectly fine. On the second day she was here, I noticed that she was sneezing every few minutes. A few days later, I noticed a little bald patch on one of her paws, and then I noticed a slightly bigger bald patch on her chest. She also has two smaller bald patches on two of her toes on her back feet (the two inner toes). Also, a few days ago, she woke up and couldn’t open one of her eyes. She had gunk in it, and we had to wipe it out for her. I think I saw what looked like worms in her butt. I also have a dog that she is always playing with. Somebody please let me know if they know what this could be, or if it is contagious, so I can keep her away from my dog!