"Sometimes a role might be difficult on my throat"

Tara Strong is an accomplished voice actress, so it is likely that the quote is describing the strain that can come with carrying out a voice function. Voice acting can be physically demanding, as it requires the use of the throat and vocal cords to produce the wanted sound. It is possible that Tara Strong is describing a particular function that she has actually taken on that is especially challenging on her throat. This might be due to the length of the function, the intensity of the performance, or the vocal variety needed. It is likewise possible that the role needs her to utilize her voice in a way that is not natural for her, such as speaking in a greater or lower pitch than she is used to. Whatever the case, Tara Strong is likely describing the physical pressure that can feature carrying out a voice role.