My daughters have been on anything from 7.5 mg to 25 mg. 25 mg is usually considered the highest dose, though I have heard of rheumatologists occasionally going up to 30 mg.
10 mg is a fairly low dose. My older daughter is on 15 mg. She is also usually a bit tired and nauseous the day after the shot. She takes folic acid daily and Zofran the day after the shot.
Is your daughter on folic acid? If so, what dose is it? Some kids need more to prevent side effects. My kiddos started on 1 mg daily, but it wasn't enough, so we went up to 2 mg daily.
There is also Leucovorin which is folinic acid. Rheumatologists seem to use it more than GIs for some reason. It is considered a "rescue" drug for MTX - used a LOT with cancer patients who take much higher doses. It is usually given 12 or 24 hours the MTX shot and can help with side effects.
However, it's usually given with much higher doses of MTX, since it does impact efficacy a little bit. My girls were on it when they were on 25 mg of MTX per week.