Flight Safety, you have a very good understanding of a lie that's been told to us for some time.
The question is not "Can you ever feel a centrifugal force?" (we all know that it can be). The question is, "Is centrifugal force a real force?"
For a centrifugal force to be felt, the "feeler" must be rotating and off the axis of rotation. That means the feeler is accelerating. Although the force is felt, there is no effort that creates it. The dumbell in your example is not pulling on your muscle, your muscle is pulling on the dumbell. This is where many get confused and say that centripetal and centrifugal are equal and opposite. A/ They can't be otherwise their would be no net force and thus no acceleration, and B/ They can't be measured in the same reference frame.
If you weren't aware that you were spinning on a merry-go-round, then you would be very perplexed on why the dumbell seems to repel your body. You wouldn't see an object firmly attached to the floor of the merry-go-round and think, "If I pick that up, I must supply the required centripetal force in order to keep it in it's current radial position."
If you were aware that you were spinning on the merry-go-round, then you're actually thinking from the stationary reference frame. In that frame, you're not surprised that the dumbell wants to pull away from your body, you realize it wants to fly in a straight line, and you must pull on it to move it in a circle.
Sum up:
- Centrifugal can be felt but only in a reference frame where the laws of inertia don't hold.
- Centrifugal force isn't created by any effort.
- Centrifugal is an apparent force.
One more thing, Newton's second law according to Newton is that a force is the instantaneous rate of change of momentum. The F=ma comes out of that for non-relativistic physics.