How does one distinguish between homographs in Chinese?
Yes, this word has two different pronunciations.
便宜 pián yi means:

[adj] cheap, inexpensive
[noun] benifit, interest, which you are not supposed(allowed) to get.
[verb] to make sb get that benifit

便宜 biànyí means:

[adj]convenient

Because these meanings are different significantly, I don't think we'll get confused. Also, biànyí is a written, literature ,classic word, so you won't meet it in most cases. Instead, we'll use &quot;方便&quot; in that case.
In your example, I don't think 便宜 is used correctly, no matter how it pronounces. You may want to say:

我的大学学费很便宜。 The fee of my university is very cheap.
我的大学上网很方便。It's very convenient to surf the web in my university.