You can be born with aptitudes, like rapid healing and similar abilities to mediums like you say you have, but you can not be born a witch. It is not something that runs through bloodlines, as Beltran states:
" Witchcraft isn't something that runs through bloodlines like blue eyes. Being a craft, it's more like painting, carpentry, or cooking. Whole families may share and pass down the art, but new offspring aren't born a painter, carpenter, or chef.
You could come from a family of carpenters, you could know a lot about carpenty just by being raised around it. You might even be able to hang a shelf. But until you pick up the tools and learn the skill, you are not a carpenter. "
Your abilities sound more like those of a psychic medium. Your ability to 'connect with spirits' might be underdeveloped, unfortunately I do not know anyone who teaches in that area, but If you're curious to see if you are one then here is a good site to start at: http://www.psychicsolutionsbylynne.org/7-ways-psychic-medium/