How's your son doing now? How is he tolerating the Methotrexate? I just wanted to say that most doctors give MTX as an injection when the dose is 25 mg (that's the max dose used for Crohn's and autoimmune arthritis typically). It is absorbed better and most kids have fewer side effects with the injection (though some do prefer the pills - it's very individual).
Both my daughters are on MTX with biologics - one is on 20 mg and the other is on 15 mg. In college, both took it on a Friday or Saturday so they had a day or two to recover. Folic acid every day helps prevent side effects and if your son does get nauseous, then taking Zofran can help a lot.
They both inject it - it's a tiny needle and the shot is pretty painless. Both do it before bed so that they can sleep through the side effects. One of my daughters takes Zofran 30 minutes before the shot to prevent nausea and the other doesn't need that. They both can take Zofran the next day if they are nauseous but typically don't need it.
My younger daughter was on Humira every two weeks without much benefit and then we moved to weekly Humira and that helped, but not enough. Then we added MTX and it took 8 weeks or so to kick, but that plus weekly Humira turned out to be her magic combination!! She went from being completely miserable due to symptoms to being a normal teen!! It really can help with biologics. I know your son is discouraged which is why I wanted to tell him her story.
My younger daughter has severe arthritis in addition to Crohn's and while she hasn't been on Stelara, she has been on 9 or 10 biologics and has needed many of them at very high doses. We have often had to appeal multiple times, then her doctors do a peer to peer review and if that doesn't work, we have once or twice had an independent review board look at her case. It has sometimes taken months to appeal to get the higher dose or frequency, but it usually does work - your doctor just has to be persistent.