Held up means that something makes someone late. So, for example: I was held up, and arrived late to the meeting.
Warning: "Held up" can also mean "robbed." This is used when a person has a gun or a knife and robs you in the street. It does not mean when someone steals something without you knowing.
Held back can have multiple meanings.
First, held back can mean not passing in school and being required to repeat a year. For example, a child does poorly in 5th grade and has to repeat 5th grade. That child has been "held back."
It can also mean "to limit." For example, "I held back my complete strength when I hit him so that I wouldn't kill him." Another example, "I was always successful in business. However, my family held me back. I would have spent more time working and been more successful if I didn't have a family."
It can also mean "not to act/to be physically restrained." For example, "I was going to hit him, but my conscience held me back/but my friends held me back." The first, you did not act. In the second, you were physically restrained.
I hope that helps!