If I apply a force on a block, the block, by Newton's 3rd law, applies an equal and opposite force on me, call it reaction. The reaction, which is also a force, should also apply an equal and opposite force on the block and that force should also cause an equal and opposite reaction on me again and this forms an infinite loop. How do you explain this? What are its consequences or how do you just prove that this does not violate anything?
The equal and opposite force that the reaction force applies, is the original force.
Newton's 3rd law states that forces come in pairs - like shoes. That shoes come in pairs does not mean that there are an infinite loop of shoes. Likewise there is no infinitely loop of forces. They just come in pairs. If you see a force, you know that its opposite-but-equal counterpart also exists. And the counterpart to the counterpart, is the original force itself.
(By the way, you cannot ever know which is which. Action and reaction are just words we invent and that we use to make it easier to talk about it. Both forces of the pair are there at the same time, one was not "first". Is Earth pulling in you with a gravitational force first, and you are pulling back in Earth with an equal gravitational force second? That doesn't make much sense - both force started working simultaneously.)
The force you apply on the block and the force the block applies on you constitute an action-reaction pair. That's all there is to it. In other words, according to Newton's third law, forces always come in (action-reaction) pairs. One force doesn't precede the other, and neither is it caused by the other. They just exist "simultaneously."
The force applied on you by the block doesn't cause "again" an additional force on the block. Its reaction is simply the force you apply on the block.
The forces are equal, but the forces (the action and the reaction) are acting on different objects. The forces do work on the respective objects. Hence, there is no other force generated thereafter.
For example, when a fly strikes a moving car, the they both strike each other with equal force, i.e, the car also strikes the fly with equal force. The force on the car (the large mass) by the fly is negligible and causes no disturbance in its path, the same force applied by the miniature fly (way smaller mass, but equal acceleration) causes it to turn into pulp.
Same can be applied to a man shooting a gun. Here, if the gun isn't handled carefully, it is capable for serious injury due to the enormous recoil.
Gun recoil (When not handled carefully) : https://www.youtube.com/watch?v=py_2F5u0OFo