If I want to continue using an inter rhyme after I just used one, does it have to rhyme with the other internal rhyme? If I want to continue using a regular rhyme after the internal rhyme, does it have to rhyme with the internal rhyme?
Short answer - no to all. Longer answer below:
If I write a rhyme in a line
"I put a fish in a dish"
or "I set a hog on a log"
So long as the scheme makes sense
and it doesn't make your teeth clench
You can do what you like.
There are so many different types of poetry and so many ways that poems can be structured, that in the end all that really matters is that you be poetic - or in other words, freed from the constraints of prose.
I hope I've planted a seed
and not made your eyes bleed
as I wend and wind this answer mine
across the vast poetic sea
Letting the push and pull
of wind and water and wave and gust
get to the germ, the thrust, the grain, the notion
it's all good when coming from the poetical ocean
(This all assumes we're meeting your teacher's expectations on what poetry is and what rhyme is supposed to do!!!)