Personalised Messages / Chat UI DailyUI

Quick short personal case study :

There's a problem I or many of us face while chatting simultaneously with online friends.
"We have to get back to the Home Screen which shows all chats and then click on the other ongoing chat."
The common solution or hack to this we all apply is by clicking on the incoming notification as soon as it arrives. It's a simple quick trick to bypass the home screen but its BAD UX.

SOLUTION to that is I created a recent chat bar on the top which shows the number of messages received on an ongoing chat in Green and other chats in Orange.
Clicking to any chats on that Top recent bar quickly get you inside the other chat bypassing the home screen.
Is it Good UX?
Looking for a lot of feedback.
Cheers!