Buddy, I'd say don't fret too much about the treatment result.
You probably won't know one way or the other for a few months. And an early scan will be a waste of time. If the doctor refuses you, don't suspect him of hoarding hospital resources or anything - the simple fact is, those scans get confused by inflammation.
Traditionally, the scan is done about 3 months out, and even then, there's a significant percentage that score false positives - ie, the scan is unable to determine whether or not the glowing bits are cancer or inflammation.
For me, the re-scan was around 5-6 months, and I got the all clear.
So yeah .. my opinion .. you're jumping the gun, you need to be patient and wait this thing out. You're clearly taking the fight head-on, and that's admirable, but fighting cancer can also involve managing expectations & anxiety, as much as surging forward, ticking all the boxes, compliance, etc.
Mate, I'd suggest not to worry too much (if it does genuinely feel like it's growing, ask your doctor, but hey, that might be swelling due to nerve damage as well, just seek their opinion and if you don't trust it, a second opinion). If they shrug if off as nerve damage or whatnot, just don't feel "ahh that's bullshit, I need a definitive answer !"
Because yeah, your body has suffered a massive insult, and either way there's no definitive way excluding a biopsy, to assess treatment success that early in the game. And a head & neck biopsy, especially after all that damage, is (as I'm told) tricky business.
Just a comment to add a little context, of course it's your life and you can balance things how you see fit .. but I'd suggest to spend the next couple of months allowing yourself rest, taking as much protein and nutrition as you can, and managing your mental health protectively.
