Itchy chin/scratchy throat w pain in throat & chest w a very painful cough w yellow mucus I allergies/asthma could new pup be causing flareups?

Can be. Can be allergy but a yellow mucus is not very typical. Would check fever and if no fever give can wait a little. Stay away form possible allergen.
Possible allergy. Your symptoms could be allergies/asthma due to the new puppy, although yellow mucous also suggests a possible infection. An allergist can help determine if this is a reaction to the puppy or other allergens and help you find relief.