This is not an easy question to answer because it involves subtle changes in meaning.
Let's start with the example in your title. The phrase "among other things" or a variant simply implies that what is specified was one of several things, the others of which are not specified. "In college, she studied French history among other things." The point here is to specify that although she studied French history, she studied other things as well. It is not limiting.
Now let's move on to the first example in the body of your text. This is not idiomatic because here you are specifying other things. "In college, she studied French history while also studying biochemistry." The point here is to emphasize for some reason her study of French history while recognizing the specific other field that she concentrated on simultaneously. It does not necessarily imply that studying two different fields simultaneously was particularly difficult, however unusual such a diversity of fields may be.
If you want to emphasize the difficulty of doing one thing while simultaneously doing others, you use "despite." Here you can be specific or non-specific. "She graduated from college with honors in four years despite all the other demands on her time" or "She graduated from college with honors in four years despite working full time and caring for her invalid mother."
EDIT: Based on the comment below, you may use "alongside" as a synonym for "while."