Here's the deal ... DT was leaving the E. Jean Carroll defamation trial on Wednesday in NYC when he raised a hand to wave to his loyal followers who were stationed outside the courthouse ... and something bright red caught the attention of photogs.

It's hard to make out exactly what it is -- but some thought it looked like blisters or sores of some sort ... and of course, the internet went crazy with theories when they saw it, with many attempting to diagnose the former Prez with just about every ailment under the sun.

Interestingly, he surfaced from court later the same day on Wednesday ... and the so-called red hand was a little more normal-looking that time around. It was very, very weird.

Anyway, we talked to some folks and sources tied to the Trump campaign are telling us a different story than what people think they saw in the OG pic. We're told the only thing that was afflicting Trump that day was a simple paper cut, and he accidentally spread the blood around his hand. Yep, that's what the Trump camp is saying here ... just a little nick.

While that might sound hard to believe, it might actually be the truth -- again, DT came out with his hand seemingly cleared up and free of any abrasions ... so maybe it was just blood.

BTW, he was out again in public Thursday ... and there was no sign of any redness on his right hand from what we could see. As we reported, he attended his mother-in-law's funeral with Melania and his son Barron Thursday morning.

We're in the home stretch of the Republican campaign now ... every little detail's gonna drive the public freakin' crazy -- especially for a guy who loves talking about his hands like ex-POTUS.