Keep getting this DirectX error.

The GTX750 TI does support DirectX12, but only DirectX Level 11_0.

Built on the 28 nm process, and based on the GM107 graphics processor, in its GM107-400-A2 variant, the card supports DirectX 12. Even though it supports DirectX 12, the feature level is only 11_0, which can be problematic with newer DirectX 12 titles. 

In this case, Apex Legends requires feature level 12_0 at the minimum for DirectX12.

You can still play the DirectX 11 version when launching the game via Steam, which would look like this:

Unsure how it would work for the EA App, you'll likely have to set that command in the error message you got as a launch parameter.

This can be done by pressing the "Manage" button when you have Apex open in the EA App, then going to "View Properties" and then pasting this: 

-anticheat_settings=SettingsDX11.json

into the Advanced Launch Options and then press the "Save" button
Which should look something like this:

Then you should be able to play the game again.
Though do keep in mind, as mentioned in the error you got, it's possible they might drop support for DX11 in the future, so it might be best to upgrade your GPU if you are planning to play this game in the future.