This is an issue that resolved itself, but I figured I might as well create a Topic about this in case anyone else has encountered it, and as a way to share the interesting experience.
I brought my Power Armor into Corvega Assembly Plant, took a few blows and narrowly avoided a grenade blast, but no damage was done to my armor and no limb injuries were sustained. However, my health was nearing the halfway mark, so I used a Stimpak before proceeding any further. It didn't seem to do anything. I shrugged it off, then walked up to a Terminal. Couldn't access it. Got out of my armor and tried again - still couldn't get the hack screen to come up. Then I looked at my health again and noticed it was still low, so I used another Stimpak. Then I finally noticed that my health kept draining for no apparent reason. In the end, I decided to try hopping into a vacant bed, slept for one hour, and...the issue was fixed, and was able to access the Terminal as well.
I don't think there was a head injury involved, as no such injury notifications came up during the entire firefight. I believe it was just a weird glitch, and am glad it was something fixable and not permanent.