Two weeks ago I fried the dryer outlet and plug and replaced both. I made a short 90 second video explaining the problem https://www.youtube.com/watch?v=55AfK_y1RGo Here's the background: We ordered a new dryer and when it arrived the plug was not connected. I wanted to check to make sure it was the right outlet for the plug before I connected the plug to the dryer, so I plugged in the (disconnected) dryer plug to the outlet. It sparked and I turned off the electricity. I realized this was because the dryer plug connection points were all crossed in the packaging. So I changed out the outlet and ordered a new plug (also fried). I tested with electric meter ONLY on one side of the 220V and it had power so I thought I was good to go. The dryer turned on and we looked like we were headed for the promise land 🌴 only to find out that the dryer ran for 5 minutes and shut off. This happened 3 times. So we unplugged, and I rechecked the voltage and only one side (THE BLACK WIRE) had power (120V). The other side (RED WIRE) did not. What's strange is we checked the breaker box and BOTH sides had power. 🤔hmm... Could the RED wire in the plug have gotten damaged? Do I need to replace the entire cord running from breaker box to outlet.
First, you need to change that to a 4-prong socket (NEMA 14-30) and cord (and I bet the dryer came with a 4-prong cord). The 3-prong type is obsolete and dangerous. If the neutral wire loses contact, it will energize the chassis of the dryer - and I bet the washing machine is grounded, isn't it? :) It's a matter of time before you touch the equipment in the wrong way, and blammo.
How likely is a wire losing contact? It's happening to you right now.
That plug has been retired for decades - it's only sold today as unit replacements for houses which can't use a 4-prong. You definitely can -- there's a ground wire inside that junction box.
Now, if the ground wire is already tied to the metal box, then you will not need to run a ground wire to the 4-prong socket -- it will pick it up automagically via the hard flush contact with the metal box.
As far as your immediate problem, it's not defective wires. It's unbelievably unlikely for a momentary surge to destroy a wire. However, it's very common for surges to take out wire connections (where they meet the screw). We presume the dryer end is good because you just redid it...
... so that leaves the breaker end. Your test measured voltage to the breaker screw, not the quality of the wire connection at that screw.
Don't forget to check the neutral wire inside the service panel... everbody forgets that one. Remember, a loose neutral with a 3-prong socket creates the condition that will kill you so treat that dryer with fear and respect until you have either installed a 4-prong outlet, or have positively cleared this problem.