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.