Give the three colours different roles: lead, companion and small accent. This makes a palette easier to use than choosing three unrelated favourites.
Test the roles
Look at the palette at nail size. The accent should remain visible but should not obscure the difference between the two larger colour areas.
Reduce detail first
If the result feels busy, remove a motif or reduce the accent area before replacing all the colours. A simpler layout can make the same palette work.