Just a couple, really. Dydd wedi doesn't mean anything;
I didn't think it would. I was just making a guess based on the form blwyddyn wedi
, which seems to mean "the next year".
the word for "tomorrow" is yfory. Byddaf is technically correct, but nowadays most people say bydda (and the same is true with other 1S future verb forms).
So the 'f' is dropped in spelling as well as speech? I didn't know that.
You don't even need an explicitly future form, however; like English, Welsh can use the present progressive with future meaning.
That makes sense.
But this is neutral, i.e. "I'll be going to school tomorrow." If you want to express that you have to go to school, you would use a construction with rhaid, i.e.: Rhaid i mi fynd i'r ysgol yfory.. (Rhaid isn't a verb; the verb in the sentence is technically bod, but it's usually dropped in the affirmative.)
So there would be three possible ways of writing this:
a) Bydda(f) i'n mynd i'r ysgol yfory. (neutral)
b) Dw i'n mynd i'r ysgol yfory. (neutral)
c) Rhaid i mi fynd i'r ysgol yfory. (necessary)
I think the appropriate one here would have been c), as the point was that I had to go to bed because I had to wake up early for school tomorrow. (Not sure what "wake up early for" would be.)