Tricky!
This wont be a definitive solution to your issue but more like 'background info' to try and help you.
There is a lot going on here and a complete mixed bag of colour profiles.
To answer your 'revised' question from the video on finding the colour profile of an image:
Use the Info Panel in PS to display the current colour profile of the active document...
This is how I have my Info Panel set up, it tells me more useful information than the default setting.
I also set the Info Bar to display something more useful than document size too..(Arrowed).
Now, the mixed bag.....when you recorded your video it was probably saved with the sRGB colour profile.
To add to that, even if it wasn't, most browsers probably use sRGB anyway....so the end result WE see will more than likely be in the sRGB colour space.
From this you can see that viewing your video is not going to be exactly the same as you see it on your monitor (unless every process uses exactly the same profile). In addition, your monitor will also be using its own colour profile too.
Not only that but we all know that YouTube likes to mess around with anything it gets its hands on so again this could be yet another colour profile....who knows?
The upshot of that is that as an outside viewer watching a video in a browser (with its colour profile), of a video that has gone through the washing machine called YouTube (with its [possible] colour profile), of a recording made on an OS (with its colour profile), of a Photoshop document (with its colour profile), of an image (with its colour profile) that could have (and looks like it has) already been through several colour profiles already.
To back that up the 'circular' images look to be the same image with just different colouring (and cropped a little differently).....so it looks like those images have already been through some image editing program before you even got them.
The usual work-flow for Photoshop is to edit in Adobe RGB (1998).
If the image you have isn't in that colour space then you can convert it to Adobe RGB (1998) (or whatever ) using:
Edit > Convert to Profile
You can also set PS up to warn you if images don't match your working profile (And many other things) by using:
Edit > Colour Settings
When saving images out of PS to be used for the WEB (As in your case), then ALWAYS use the 'Save for Web...' option.
This will not only enable you to optimise the image but also set it to automatically save in the sRGB profile (which is what most browsers use).
The 'Save for Web...' window also allows you to preview the image in a browser of your choice so you can compare it before committing to saving.
Just to confuse matters even more....if you use FireFox as your browser of choice you can change the colour profile it uses too.
In Windows machines colour profiles are located here:
C:\Windows\System32\spool\drivers\color
In FireFox you can enter...
about:config
...in the address bar, and once you promise to be careful enter...
gfx.color
...into the search bar at the very top of the page.
This will give you 4 preferences you can change, to set the profile change the following:
display_profile (default is blank)
Double click this preference and enter the FULL path to any of those profiles at the location above. (sRGB if you want to make absolutely sure that's what FireFox is using).
I don't recommend keeping this to anything else than the default (blank) or sRGB but for testing and comparing it could be useful.
Sorry none of that is a definitive solution but maybe it will help you in some way.....when using images that (to me anyway) look like they've already been edited you're already on the back foot......making the best of somebody else's bad job.
Regards.
MrTom.