Question about index/constraint definition in a table

I have a table as follows:
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Table Artist Colaborations
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* car_id (integer field, primary key)
* car_song (integer field, foreign key, foreign table is a catalog of songs)
* car_artist (integer field, foreign key, foreign table is a catalog of
artists)

So, I added 2 indexes to improve JOIN in queries:
1. An index for car_song which accepts duplicates.
2. An index for car_artist which accepts duplicates.

Now, the combination of "car_song + car_artist" cannot be duplicated so I
think that adding a constraint on these 2 fields is the solution.

My question: Is this the correct way to go?

Respectfully,
Jorge Maldonado