Okay, noticed a few more issues.
if (isset($_SESSION['highschool'] == $value) {
Your isset is out of place here. I imagine you want it to look like this
if (isset($_SESSION['highschool']) && $_SESSION['highschool'] == $value) {
The same goes for the next if statement you have.
You do also have an error in your query statement. I'm not sure if you're familiar with the workings of sprintf, but your query should only take two variables, user and password. You're giving it three (table name).
One bit of advice I also have. Whenever I do a header("Location: ..."), I always do an "exit();" immediately afterwards. This makes it so that the remainder of the page doesn't have to execute, possibly displaying html, which is just going to ignored with the redirect anyway. I mention it because when $value is either highschool or college, you'll end up doing two separate header calls (the second being "$next_page", when you only need the first one.
Oh, and I mentioned php.ini, but I wasn't specific about variables to look at. In specific you should have "error_reporting" set to "E_ALL", and "display_errors" set to "On".