Help with tire size

First picture is my jeep with the 35” and second and third pictures are the 37” I’m looking at

@Peyton S have you ever ridden a 10 speed bike of any kind? If you have, you know how difficult it is to start off from a dead stop in a taller gear. The same applies to larger (taller and wider) and heavier tires. The amount of stress placed on the engine, transmission, drive shafts, differentials, brakes and axles multiplies pretty significantly. While it seems an easy question, "will they fit" the mechanical side of that question is not so easy. The upgrades required to keep form breaking things rather quickly and the ability to stop is really compromised.

In addition, "will they fit" is not just will they fit in the wheels wells with your setup, since it is a wider tire as well, are your wheels offset enough to allow the additional width? Factory wheels absolutely do not. Some might say use a spacer between the wheel and hub. Bad idea. All of that rotating mass moving, flexing, turning will break an axle rather quickly.

Unless you've got somewhere in the ballpark of $10k to upgrade everything to run that big a tire, then no, they wont fit.

The new larger tires may fit. But you may have clearance issues at the front bottom corner of the rear fender wells, where your tube step bar is. If you have adjustable control arms for the rear axle you can adjust them to move the axle back a little.
If your only concern is "will they fit" and not how well they will work, there is the answer. They should fit aside for an area of concern at the bottom front corner of the rear fender well. There is also the question of backspacing, do the wheels have enough backspacing to fit tires that wide? Since you have not indicated how wide the 37's are, or what backspacing the wheels have, it would be impossible to answer.

That said, you may find that, even on the street, they 37's don't work well. They will make your gearing, whatever it is now, taller. That will reduce the performance of the Jeep, making it slower and putting more load on the engine and transmission. They will also reduce the effectiveness of your brakes. They will make steering, turning the wheels left and right, harder. That will be more noticeable at a stop or at lower speeds. They will put more loads on the wheel bearings, axle shafts, and ball joints. And it will put more load on the steering linkages and steering box.
If none of those things matter to you, have at it. Don't get me wrong, I like 37's, and run them. But I have spent a lot of money to do it right. I have regeared, upgraded the D30 front axle, added hydro-assist steering, upgraded to larger brake disks, upgraded the ball joints, replaced wheel bearings, upgraded axle shafts, have adjustable control arms, and more. I did all that to make the 37's work as well as I can. But you do what you want. I can't see it from my house.