Welcome always, I was going to reply on your thread, but since you have posted here I'll reply here.
How much VitD is in the multivitamin? It is likely not enough considering DS isn't spending much time outside. He may need an additional supplement.
Have you applied for DLA?
Have you heard of inspirative arts? They are local to you. If you do decide to go private you can search for a private psychologist on BPS and ACHIPPP.
Have you looked at ARFID?
I'm not surprised the a GP won't prescribe phenergan. It isn't licensed for this use (which is why you would have to lie that a pharmacist to get it OTC), and whilst GPs can prescribe off license they are really unlikely to in this situation. If you are going to buy something to help with sleep look at melatonin.
Is DS swallowing the mucus rather than spitting it out? My DS's have a condition that causes thick sticky mucus and if they swallow rather than spit it out it can make them feel nauseous. Also, here we are strict with medication, it isn't optional, if DS's resist we force the matter. For us the battle is eye drops, but nasal sprays would be the same. Sometimes DC can't rationalise something will help them.
Whilst it's tempting to leave him on the iPad whilst calm, for us and others on here unlimited screen access isn't helpful longer term.
Just to reiterate, don't wait to apply for an EHCNA, a MH assessment can be part of the assessment, and if you get an EHCP MH therapies can be included.
Listen to Zoo, looking after yourself is just as important, you can't help DS if you don't.