Arwen could've gone to the Grey Havens?

[Lumiel]

I'm reading LOTR for the third time right now, and I was glancing in the appendix of the third book to brush up on Arwen and Aragorn's history (since among friends I'm Arwen) and I found some info on Legolas and how he went to the Havens. It said that Legolas left for the Havens with Gimli AFTER Aragorn died, so when Arwen said that she couldn't have left to the Havens even if she had wanted to, she lied! I'm just frustrated because I believe that if she could've gone to the Havens, she should have! I understand that she loved Aragorn and all, but she still had life left to live! (a lot of it being immortal) And she could've done something great with her immense time left. Tell me if I messed up on the info or not, I think that she should've gone with Legolas and Gimli (I laugh every time I picture poor Gimli in the Grey Havens surrounded by elves!)