If electric current creates a magnetic field, and if magnetic field exerts a force in charged particles in movement, is that correct that when a current (in a coil, or something) creates magnetic field, there is also a force against the coil?
Yes, the magnetic field produced by a coil does exert forces on the coil.
Every element of the coil exerts a force on every other element which is not perpendicular to it. It exerts a repulsive force on parallel elements in which the current is flowing in the opposite direction. And it exerts an attractive force on elements in other loops of the coil which are adjacent and parallel to it, in which the current is flowing in the same direction. These are just the familiar forces between parallel/anti-parallel current-carrying wires.
There are also forces of intermediate value between elements which are inclined at different angles other than parallel or perpendicular.
As a result there is a resultant outward force on the coil, tending to increase its area, and at the same time a contracting force between adjacent loops, tending to shorten the length of a solenoid.
However, no element of the wire exerts a magnetic force on itself.
You can think of a magnetic field as an electric field from a different frame of reference (thanks to the help of special relativity).
This video explains it well.
So it all depends on the situation and of the frame of reference. This might give further info.
Hope this helps.
For a really simple example of a circuit exerting a force on one of it's elements, it's worth nothing that this idea is the principle behind a railgun: