Computer Stuck in Automatic Repair Loop

Are you able to get into safe mode?

When the blue screen with options appears click on "Troubleshoot" and select then "Startup settings"
Choose "safe mode" on next screen

Safe mode will not start any drivers that are not essential so that may give some starting clue, let us know if that let's you into OS?

If the information is helpful, I did use a dust spray to clean out the motherboard while trying to take the screw out. I may have sprayed a bit too close to the board though.

presumably not with power connected -
and what make of dust spray please - a air duster spray designed for such use or what please.

Re this

I ended up having to force it out with pliers and I was able to eventually take it out. I was able to install it just fine, but once I booted my computer back up, it wouldn't go past the boot up sequence and it eventually went into an automatic repair loop.

what happens if you remove the installed drive and then power on.

It is difficult at this stage to know what has occurred.
The M2 placement is as follows
Follow the steps below to correctly install an M.2 SSD in the M.2 connector.
Step 1:
Use a screw driver to unfasten the screw and standoff from the motherboard. Locate the proper mounting
hole for the M.2 SSD to be installed and then screw the standoff first.
Step 2:
Slide the M.2 SSD into the connector at an angle.
Step 3:
Press the M.2 SSD down and then secure it with the screw

I presume you did check that in your effort to remove the screw - you have indeed left the standoff in position, rather than placing the M2 Drive in position without the standoff

Before playing with hardware attempting to find what's wrong, I recommend you boot into linux live and see if you can find some issues.

If all goes fine, install it on trouble SSD and again see if there is a difference.

Try Ubuntu before you install it | Ubuntu

Did you follow the procedure I outlined from your manual
The M2 drive has three positions
Š 1 x M.2 connector (M2B_SB), integrated in the Chipset, supporting Socket 3,
M key, type 2242/2260/2280 SSDs:

Have you checked IF you removed the standoff by accident when removing the screw
It is not a question of uninstalling the driver

It requires you to remove the newly installed drive and check the standoff position.

Until you do that - we will not be able to determine the cause.


IMHO

Before playing with hardware attempting to find what's wrong, I recommend you boot into linux live and see if you can find some issues.
If all goes fine, install it on trouble SSD and again see if there is a difference.

installing Linux on that new Samsung Evo - even if your could - with Windows 10 already installed - would be a wrong move - without you knowing what you are doing.
Even although it is on another drive you may find out, that you have problems with the windows boot loader.

I in

stalled an M.2 when I first built my PC, so I know how to put it in

cheers
You will appreciate, of course I had no way of knowing that.
Novices sometimes remove the screw, but then do not realise there is a standoff - in position.
Some boards, come with the screw and standoff already installed in the final position slot - eg in this case 2280 on that M2 slot.
Some boards come without them installed but in the accessory pack.
Yours presumably from the manual - where I took the copy and paste from - came with it pre-installed.
I just wondered if with the difficulty you had removing the screw - there has been some manner of other problem caused.

Re this

Does the BSOD error message list which driver causing the error?

I am unsure if we have a BSOD with an error
I think we may be talking about the advanced recovery options etc - blue background screen