If person #2 tells you that your feelings aren’t appropriate because she had it worse then she is wrong. Your feelings of pain are yours, and a person should feel a friend’s pain.
If person #2 tells you that she understands pain, as she has felt pain too, that’s called commiserating and it’s something that is very much appreciated.
It seems that both person #2 and #3 are correct. Person #2 commiserated, yet person #3 understood that she was invalidating.
I would have told person #3 that you appreciated person #2 telling you about her pain because “misery likes company.”