Not going to mention brand, only that it's a one piece curve. It's a 58in'er and has started making a sharp, but faint pop about half draw. Kinda puts me in mind of sliver of glass cracking.
Sounds like in the upper limb, but I can't find anything wrong with it. No delams or cracks...nothing. Looks good.
What should I do? Keep shooting?

If you have too much wax on your string it can get a bit noisy especially in colder weather. Try wiping your limbs with a dry cotton ball. If there is an unseen splinter or snag the cotton will hang on it.

New string ?   or just heavily waxed ?  If it is not structural it could simply be that the wax is sticking and popping off the limb once it gets to that position.

Be careful and make certain it is NOT structural before you presume this though
ChuckC

Sure it's not wax on the string near the grooves. Flemish or endless loop? Cold weather and wax does make that creaking noise.

I had the same problem but it ended up being my elbow cracking. It used to happen only every now and again but now it does it every time I draw my bow.

At half draw the string is no longer contacting the limb anywhere. Can you observe/listen to someone else drawing the bow?
Can you discuss this with the bowyer and perhaps he can look it over?

It's and endless loop string with no wax near the ends. I can hold it sideways to myself and draw halfway while listening to different parts of the bow. It's somewhere in the upper limband doesn't do it alll the time, but most of the time.
Also I can drop brace height two twists and it seems to change the sound.

Sounds to m e like it needs to go back to the bowyer. He should replace it. The thought of the bow failing on you will always be in the back of your mind and if it does break you could get injured.

Look at he limbs and see if there is a twist in one.I have hade them do that when the string was coming out of the groove from a slightly twisted limb.Usuallay ou can just keep twisting it back without even using hot water.

Get it back to the bowyer ASAP.  If you can't get it to the original, have another bowyer check it out.  Definately not worth taking a chance of an injury.