Hi Tina,
well done with your translation! I am speaking from the point of view of a native, as I am not an Italian teacher. However, I think your translation is very accurate. I would keep "you better free yourself" because "meglio che ti liberi" is an advice just like "meglio che ti guardi dentro". So, again, "you better look inside" is the most appropriate translation, in my opinion, if one wants to stick to the nuance of the original lyrics.
Best wishes,
elisa