You are right: It should feel really strong at the return, whatEVER the pressure is! Here's a case where you know your pool best. If I saw 13psi, I'd be worried something was blocking my drains. If I saw 7psi, I'd be sure of it. But that's because for me, 20psi is normal and 25psi is when the force of the return flow drops---same 5psi increase as you have.

Now, we still don't know what you consider a "high" chlorine level. Nor do we know your CYA (stabilizer) level. The CYA level affects what the ideal Chlorine level is, both for shocking and for maintenance.

You can increase the range (but not the accuracy) of your OTO test kit with distilled water--only steam distilled, not ionized. Chain drug stores and supermarkets have it by the gallon. You can search our forum for the CarlD Shot Glass method, but here's how it works.
mix one shot glass of pool water with one shot glass of distilled.
Mix and pour into your test cell (the gadget with the scale). Whatever the chlorine reading is, double it.
Or, you can use 2 shots of distilled to one of pool water. Now whatever the chlorine reads, TRIPLE it! If the scale reads to 5, you can now measure to 15.
3 shot: You can measure to 20ppm!

But.....you MUST be careful measuring and mixing as your accuracy goes down with each level of dilution.

And, yes, you really do need to keep your chlorine level at (probably) at least 15ppm if you want the pool to clear. Now I opened to lime green "jello" on Saturday. It was disgusting Today's Wednesday and my water is clear. Why? I hammered it with chlorine immediately and kept at it, intending first to kill the algae, THEN clean it up. I'm now using Tri-chlor (gasp!) that I had left around because my pH is a tad high and my CYA (stabilizer) was non-existent. As a temporary fix, GIVEN MY POOL'S CHEMISTRY, they are ideal. The tabs keep a constant level of chlorine, are increasing my CYA (which I need), and lowering my pH, which I also need. So I'm not bothering to add baking soda or borax at this time, sticking with chlorine.

For another poster with CYA of 60 and a pH of 7.0, I STRONGLY recommended they stay away from Tri-chlor tabs and Di-chlor powder. They don't need a lower pH and a higher CYA level, it will make things worse. Yet it's still simple to do.

All the best,

Carl