Demodex sucks. I've been there, and it's not fun. If it's just on the head, and your pup isn't suffering too much, I would try and wait it out. It's really common in pups, and most of them can get over it on their own. The dips and things are really nasty and harsh, as well as time consuming and expensive, and often don't work anyways. Ivermectin works, but again, if the pup can recover on his/her own, that's better.
Is it localized or generalized? Localized means just a few patches, Generalized means a large area and/or all over the body. Usually pups with localized will have spots on their head/face/forelegs, and pups with generalized will have their entire heads/chest/legs bald and scabby, and some baldness/scabbiness on the back and back end as well.
In the meantime, bath your puppy with a gentle oatmeal shampoo too soothe the skin, not too often, you don't want to overdo it. Aloe vera gel can help with discomfort too.
Demodex is caused by a lowered immune system, so you want to boost his/her immunity. This is done through a good, quality diet, lots of TLC, keeping him/her warm and dry, etc. Don't get your dog any shots until this clears up a bit, vaccines often trigger a demodex break out. Your vet should not have given the pup the shots he did if the pup has demodex - you may want to change vets. Things will probably get a bit worse before they get better due to the vaccine making the immune system work harder.
Good news is demodex is not contagious, and is almost always cureable. My girl had two patches on her face for what seemed like forever (over 6 months). What finally cured her was a combo of putting her on Revolution flea control (kills sarcoptic mites and does help control demodectic mites) and switching her to the BARF diet. Today, her hair is finally grown back, and there is no more visible scarring.
Hope things go good with your pup - welcome by the way!