1960 Jefferson Nickel Help!

I think it is a proof all day.
The rim edge toward the interior of the coin is sharp and at an almost perfect right angle continuing along the interior height of the rim to the practically perfect flat surface.
The fields are flat and do not rise up from the interior toward the rim or to the top of the rim.
Business strikes appear to more less curve upward and meet the rim edge past the motto.
( At least on most of the outer part of the coin )
There could also be a hit or something else on the collar and the cheek seen in first image.
I think it's a proof. I agree with spruuuu on this one. Look at his coin he showed and the fields toward the inside of the rim.

Grade it? Not if it is a proof. I have a couple here I will post later that I thought were business strikes when I put them aside. Recently going through my duplicates, I was at the same point you are, wondering if the were business strikes.
I concluded they were impaired proofs. I think mine are both 1958 Jeffersons that I am thinking about.

Actually for you, I hope I am completely wrong about it being a proof. That would be something awesome if it were a MS coin.

I quickly picked one pic out and point out that it appears struck twice as US proof coins are or were under higher pressure than business strikes which shows this anyway. This is the reason for the flat fields and more right angle rims.

Many 1960 proofs are doubled dies. get out a loupe and look at the legends and motto very closely.
You may find one of the varieties for proof doubled dies and that would put an end to it.
I am trying to work on my lousy pictures of a 1958 I have here. I can't do pictures very well.
LATE EDIT
I am sorry I can't produce a decent image here. I feel a headache coming on.

Oh well. Nothing is perfect. Look at your other proof, I think you'll conclude the same.

With your close up pics I think it's a proof.

Part of why I said what I did is that if you take a look at PCGS Price Guide & Coinfacts, having a 1960 MS-66FS means maybe a $14k coin. In proof, it only becomes a high dollar coin in PF-69 DCAM, and even that tops out at about $6k. What I mean by all of that is to point out the odds.

Beyond the odds, I have specifically been in the market for early Jefferson proofs for a little while now and that's pretty much all I have looked at. I feel confident that the coin in question is a proof. Microanalyzing the exact shape of the rim may not be a good idea.

Compare the MS-66+ I posted (not mine, by the way) and see the differences in strike quality across the board. Also note the lack of Die Deterioration effects on your coin. It just...has that look of a proof. Even the haze on it from being in Mint cello looks like proof haze.

You could always submit it. I certainly don't want you to miss out on anything because you took my word for it. If that did grade something like MS-67FS, it would be a very valuable coin. I can't offer advice on what to do, just my opinion on what it is.