Here's why:
* Hoarse is an adjective describing a rough or raspy voice.
* More is used to compare degrees of an adjective, especially when the adjective has a less formal comparative form (like "hoarse").
* Hoarser is an older, less common comparative form of "hoarse." While it's technically correct, "more hoarse" is considered more standard and widely used in modern English.
So, you would say: "My voice is getting more hoarse."