Actually, Reiki does not heal with your own energies. Reiki is a very specific vibration of energy that the practitioner becomes a channel for. The Reiki practitioner does not direct or control the energy in any way, and only serves as a clear channel.
There are other types of energy healing, such as Pranic Healing, Quantum Touch, Chi Kung healing, Theraputic Touch, etc. These, however, are not Reiki. The only similarity is that they heal via touch. The way the energy is directed, and in many cases the enerrgy being used, is quite different.
It has become popular to call all types of energy healing "Reiki". This is kind of like calling all cars "Charger".