It is standard to deworm twice when a dog has worms so I wouldn't blame the vet for that.
However, it would be totally expected for him to have demodex (mites) with a weakened immune system. I would not give Ivermectin because that will further depress his immune system. I would also stay away from antihistamines (I guess that was because he suspected allergies?).
My dog had it twice (between 1.5 and 2 years) and got over it without any medication. My vet said that it's very common in dogs under 2 years old and unless it's very widespread it shouldn't need any treatment except boosting the immune system. I did use NEEM oil on Rafi's demodex and that killed the mites pretty quickly. However, I wouldn't use that if the spot is right by the eyes.
In your pup's case I would think that a good diet, fresh water and getting over the worms would resolve the demodex. I would add a good, refrigerated probiotic to help his gut heal after the worms and worming meds.
Ruth & the 4 Legged Rescue Gang
Rafi the malaroo
Gio & Varda, the krazy kittens
....In my heart: