Told cadets off, now I feel terrible. Any advice?

This is a bit long. Sorry in advance.

To get right into it, this parade night, we were practicing for our upcoming annual formal inspection (AFI). I was leading a squad when practicing our marching, and as I was marching at the front, I obviously could not see behind me - this is quite relevant.

As we were marching, I heard the cadets whispering to each other and a few were giggling. I assumed that they were messing around - I couldn’t hear what they were saying very clearly - and told them to stop talking/giggling whilst marching. It happened a couple more times after that and I told them both times to pipe down.

Once we stopped for a break, I pretty much ripped into them before falling them out. I asked why they were talking despite me telling them not to, was met with complete silence, then started telling them that, if they did that during our actual AFI, they’d be letting everyone on the squadron down (the OC, deputy OC, other NCOs, and themselves). I reached a pretty high volume and at the time felt like it was justified, because they had repeatedly not listened to my instructions and had not told me that they had a valid reason.

During the NCO meeting later, an SNCO told me that she’d been approached by a couple of the cadets I’d shouted at. They told her that the reason some of them were talking was because they were trying to correct cadets out of time and calling out cadence (due to me not being able to see the flight, I wasn’t aware of cadets being out of time). I was obviously very embarrassed upon hearing this, because I was under the assumption that they were messing about whenever they whispered to each other.

I feel like I was justified in telling the squad off because some of them WERE messing about, but a lot of the squad weren’t really doing anything wrong, and I feel horrible for shouting the way I did at them just because I was annoyed at them. Any advice at all is appreciated.