FL who's antisocial and doesn't talk very much

Yo that’s me.

A drama about my life. Let me get the script started lol :D

Ruby Ruby Love 

Marry Me! 

Also maybe Let's Date, Professor Xie? FL is very smart and very awkward when it comes to socializing/romance.

Heart To Heart https://mydramalist.com/11582-heart-to-heart

You'll also find the tag "Shy Female Lead" with this one.

Just a few recommendations... Been some time since I've watched a few of them, but FLs may fit what you are looking for. These are dramas where FL is called antisocial / shy: 

A Little Thing Called First Love (2019)

Black (2017)

Fireworks of My Heart (2023)

My Name (2021)

That Winter, the Wind Blows (2013)

Tunnel (2017)

When the Camellia Blooms (2019)

Heartbeat (2023)

True Beauty (2020)

Oh My Ghost (2015)

Fated to Love You (2014) [this one has many versions]