Word that means bad sounding

discordant -

disagreeable to the ear; dissonant; harsh.

dissonant was my first thought, but it's not as apt as discordant for your example. I think of dissonant as something that's off, not something that's just jarring to the ear.

You have to be careful to distinguish this use of the word from the more common meaning of being in disagreement.

Dissonant "To disagree in sound.....Disagreeing; incongruent." Webster's New Collegiate. It is usually used in music, but is not confined to music. "If things don't go together well, you can call them dissonant. Dissonant voices are saying different things. Dissonant clothing choices clash. Dissonant chords lack harmony." -- vocabulary.com

Cacophony has a similar definition in both the American Dictionary of the English Language, 1828 by Noah Webster and Webster's Revised Unabridged Dictionary 1913. The latter has an example so I'll just quote that one to reduce redundancy:

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1. (Rhet.) An uncouth or disagreable sound of words, owing to the concurrence of harsh letters or syllables. Cacophonies of all kinds." Pope. "

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Aside from the rhetorical use of the word, it also has specific medical and musical senses which are less relevant here. Unfortunately, I do not think people are as careful to use the word in as specific of a sense these days, so it may just be understood as simply sounding bad irrespective of context. It is a shame, given how much more useful specific words are.

In more recent years it seems to have gained the adjective cacophonous, with the adverb cacophonously, which are the fifth edition of the American Heritage Dictionary of the English Language.