UPDATE:
I FINALLY figured it out! All that was happening was there was that little 3-block loading bar thingy in the upper right-hand corner of the posting window right next to the settings cog and I didn’t notice that it was still loading for a while after I had posted images but all it took was a bit of waiting (about 20-30 seconds) and then finally the bar stopped loading and the blue posting button undimmed itself and I was able to do it!
Still not sure why that happened, I mean in the past I never had to worry about that loading bar, I never actually realized it was up there! I just waited for my images to appear in the window and then the blue button was ready to be pressed. Well I guess Tumblr must be working slow for some people or something. Still odd though how I had that same problem on 2 different computers, 3 different browsers, and 2 different wi-fi connections. Perhaps by chance BOTH my wi-fi connections just didn’t have fast enough internet…
Oh well, at least I’m able to post images again.