How to solve outdoor drainage issue?

I have this drain (white circle) behind my house and when it rains heavy it tends to flood.

Red and blue circle are two gutter pipes that go into the ground and we think these three drains/pipes connect to each other.

When I cleared out blue circle and filled it with water, we saw the water push out into the white circle.

I have no idea what the drainage situation is and it seems like white circle is down hill which seems crazy to me because it is impossible(?) to push water up and out.

What are my options to figuring out my drainage situation and alleviate this flooding problem? Should I be looking into a landscaper? an engineer? I had some people come out to look at it and quote me 875-1000 but they could not guarantee the flooding won't happen.

Thank you!