I am also able to feel energy from stones/crystals when I hold them, as are many empaths, I think. I have not been an awakened empath for very long (a few months and was delighted when I first felt the energy). If you enjoy and are passionate about stones and crystals, this just deepens your connection to them, and to the earth as well! I am also left-handed, but I feel the energy stronger in my right palm, which would normally be a lefty's receiving hand, while the left hand would be the giving hand (that's what I've been told anyways). From what you say, though, this must not always be the case:)
If you are enjoying your newly felt sensitivity for the energy of the stones/crystals, I would recommend meditation with crystals/stones. It opened me up spiritually and it may do the same for you, if that is what you are seeking!
Enjoy your journey and your stones and crystals.
As you begin your journey as an awakened empath, you start to notice your sensitivity, in general, increase, and your senses also become much more sensitive