I would not say it was normal. I think if it were me, I would ask my physician what was gonig on, it is always a good idea when heart related pain is present, to have it checked, always a good idea to be safer than sorry.
It's a new thing, only started when I caught my mother's cold. I don't sneeze on my own, so I have to tickle my nose hairs with a rolled-up tissue to clear my airways.
These forced sneezes send pain shooting through my forearms. Not sure if it's the bones or the muscles that hurt. The pain is what you'd get if you planked your arm & dared a friend to karate chop it. Also, it lingers & spreads a little to the muscles in the upper arms.
Many suggest this only happens to physically weak people unaccustomed to exercise.