Hello!
"Besides" is translated better as "not only that, but (also)"... or "apart from that." Take a look below for examples:
1. We can �t go to the beach today. I �m not feeling well. Besides (that), it �s raining.
2. Maybe we should just go home. It �s too late to get a good seat in the movie theater. Besides, I need to save money OR I need to save money, besides.
3. I teach two nights a week (less important) besides teaching full-time (more important) during the day.
As you can see, "besides" introduces or modifies a secondary or less important idea or fact. It also requires its own verb or gerund. In your book, there is no verb between "her" and "her brother." If I wanted to write the example sentence using "besides", it would look something like this:
"I helped her and her brother, besides, but neither one even thanked me."
This communicates the idea that I did not have to help her brother as well as help her, but I did it anyway, which makes it extra disappointing that I received no thanks.
As well as, on the other hand, gives equal weight to both ideas, instead of giving more weight to one versus the other. It works like a fancy version of "and".
Example: Following the accident, I was nervous as well as confused.
I hope this helps!
Zoe Morosini
USA