Beautiful Gong Shim (2016)

I feel like the family situations in these dramas are very similar.
Also the love lines resemble each other.
There's also a hint of mystery and crime solving in each where the hero acts in the same way though not through the same methods.

Both dramas are romantic comedies with a mystery surrounding the lead characters. The ML in Gong-shim like the FL in I wanna hear your song experiences a traumatic event which leads to them having amnesia. As the storyline develops the lead characters aim to find the truth of what happened in their respective circumstances.

Beautiful Gong Shim seems to be comedy/romance with some drama and Can You hear my Heart is drama/romance with some comedy. While Drama/romance with comedy is quite different from Comedy Romance with some drama, but I think you will find both dramas romantic storyline satisfying.
What they have in common is the actor Nam Goong Min playing a lead role that is wrapped in mystery pertaining to his childhood/parents/identity.

The 'ugly' and clueless girl has to deal with her piteous day to day while she tries to find her own dream. The female lead is also constantly compared to her more beautiful and successful sister/best friend.

Both main characters are "ugly" and the plots revolve about them getting their lives on the right tracks,