You say that Arnica should not be taken internally but I was recommended
by my doctor to take it in pill form before having rhinoplasty. I got
the 6c strength and have to take 5 twice a day.
Indeed, while many herbs are safe, arnica is not one of them. People taking it internally have died. But what you are taking does not contain any arnica, because the "c" indicates it is a homeopathic remedy. So at least it won't hurt you.
Homeopaths believe that you can dilute an herb to the point of nonexistence in their preparations. They believe the water contains the "memory" of what was once in it. This is an 18th century mystical belief that has never been proven by any scientific study, although scientists have tried to proove it and failed repeatedly. One French study published in Nature, where even the editors took the unusual precaution of saying they did not believe it but wanted people to try to at least duplicate the experiment, suggested that something might be going on, but the researchers were later found to have thrown out all the evidence that did not support their theory--they just said it was "bad data", although there was nothing really wrong with it. In science, you aren't allowed to throw out data that doesn't agree with your pet conclusion. That is called "data selection", and if you do it knowingly, it is a type of fraud.
Nonetheless, a lot of people still cite this work as evidence for homeopathy.
You would have to drink a volume of the solution as large as the planet Earth to get one molecule of arnica, so you don't have to worry about any arnica in your preparation. For this reason, I don't personally recommend homeopathic remedies, even though they are very popular.
I hope that helps clear things up!