Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that your 4 month old puppy Boogie is extremely itchy.
Dogs don't really get heat rash.
Dogs are rarely affected by plants the way that humans are. Poison ivy, Poison Oak, nettles and other irritant plants just don't seem to have the same effect on them. They rarely get even mildly itchy from exposure. They are however sensitive to the effects of the Wandering Jew plant, so if she's been exposed to that then that can make her skin quite irritated and itchy.
In young puppies the most common cause of very itchy skin is mange, especially sarcoptic mange, but demodectic mange with a secondary bacterial infection can be itchy too.
Cheyletiella skin mites, also known as walking dander mites, can make them very itchy but tends to found along the backline, causes large amounts of dander and seldom causes red or raw looking skin.
Fleas, especially heavy infestations can make a young dog mildly itchy if they aren't allergic to the bites. But flea bite allergy can lead to raw, red itchy skin in allergic individuals.
I think your little one should see her veterinarian for a skin scraping to look for skin mites.
In the meantime at home there are some things you can do to try to help her.
You can use a combination of antihistamines and high doses of omega-3 fatty acids to help with those (they also help with the symptoms of flea allergy). In combination fatty acids and antihistamines work synergistically, much better than either one alone.
You can try:
1)Benadryl (diphenhydramine only don't use the combination products with acetaminophen or decongestants as they can be toxic for dogs) at 1mg to 2mg per pound of body weight or one 25mg capsule per 15 to 25 pounds of body weight orally every 8 hours.
OR 2)Claritin (loratidine) at 5mg per 25 pounds of body weight once or twice daily.
OR 3)Hydroxyzine at 1mg per pound of body weight orally every 8 hours.
OR 4) Chlorpheniramine at 4mg to 8mg per dog once or twice daily.
OR 5) Zyrtec (Cetirizine hydrochloride) at 1/2 mg per pound of body weight orally every 24 hours. That would be one 10mg tablet per 20 pounds of body weight. Make sure it is NOT the formulation with a decongestant (such as Zyrtec-D) because dogs cannot tolerate decongestants.
Some dogs do better on one antihistamine rather than another. Give the one you pick a week trial and if it isn't working try another. Be aware antihistamines can cause sleepiness or hyperactivity in some dogs. These side effects do wear off with repeated use.
Omega-3 fatty acids are fish oil products. 3V by DVM or Derm Caps ES are good brand name products. Use the high end of the dosing schedule for your pup's weight. I recommend a dose based upon the EPA portion (eicosapentanoic acid) of the supplement as if we do that the rest of the supplement will be properly balanced. Give her 20mg of EPA per pound of body weight per day. For example an 8 pound dog could take 160mg of EPA per day.
Cool water baths with an oatmeal shampoo or chlorhexiderm shampoo (which is antibacterial and antifungal) and a conditioner with an antihistamine may help. The water rinses off allergens and the cool temperature soothes itchy skin. Do not bathe your girl for 2 to 3 days before or after applying flea control products or the bath will interfere with the product's efficacy, or before her veterinary appointment.
Please let me know if you have any further questions.