Single cell with multiple data points - searching and filtering

Hello all, I am a first time user of the forums here, so please let me know if I am doing anything wrong.

I am stuck trying to figure out the best way to organize student(s) information. In my situation, I want to be able to easily search by 3 different data points (student name, major, and graduation year) and any combination of those three. There can be up to 15 different data points (5 students x 3 data points each) for each cell. What do you believe is the easiest way to setup this data so that I can easily search/sort/and filter (or vlookup maybe?) it for future use? I have attached a screenshot as an example of what the entire spreadsheet will look like, while omitting certain information to avoid identification, of course.

Master Example Format.png

As you will see in the photo, column F is where my primary concern is. I separated "Student Name", "MBA", and "2015" (for example, with 3 different qualifiers ("," "-" and ";") thinking the easiest way would be to do a "Text to Columns" to split them into different columns when needed and just hide the columns they would fall into until that point. The problem is, for example, "MBA" would fall into potentially 2+ columns because I have multiple students in 1 cell. That would make counting the number of MBA students who began startups not impossible, but annoying.

Anyway, if you need anymore information please let me know. Your assistance is greatly appreciated!!!