Sounds like the breathing thing is the main bit for you currently. For me the advice that helped was that if your face is in the water then you should be breathing out pretty hard, almost blowing the air out, then when it comes time to turn your head and breath in you are ready to breathe in straight away. This made the breathing in part much less of a panic, and I also found that holding my breath with my face in the water was panic inducing too, so by always being in breathe in or breathe out mode the whole thing suddenly became very calm.
Once I got that sorted I did drills which helped with different parts of it.
One drill was to swim one arm at a time, so do a full stroke with the right arm, meet at the top, then do the left arm – catch ups. This allows you to focus fully on one whole cycle at a time to lock down the form and builds some glide in – glide is calming.
Another one was dragging the tips of your fingers through the water on the return when that arm has finished the pull and comes out by your hip, this teaches you not to muscle the return as you slowly drag your relaxed fingertips through the water, again this is nice and calming. These things combined get you to that effortless look as you relax on the returns, take your time breathing and have some glide in your stroke.
The other one was swimming with closed fists, this teaches you to keep your elbows up and catch the water with your full forearm which will give you that speed and power.
After a few lengths of each drill then do some normal swimming, and don’t look at the clock but do count how many strokes it takes you to do a length, the fewer the better.
Don’t both kicking, just kind of flap your legs super gently just to help keep them up in the water, they are not what’s powering you.
As someone above mentioned, once the relaxing elements of this click you’ll instantly go from being able to do 10 lengths before fatiguing to being able to casually do KMs at a time.
