I used to suffer with this really bad when I first started reading. It's really important to protect/shield yourself before a reading, as you are merging your energies with the person you are reading for. If the person is generally o.k, and just wants a reading for fun, its not too bad, but if you are dealing with somebody very upset they can drain your energy, and/or you can absorb their emotions especially if you are a very empathic person . Which most people who read tarot usually are.
I would spend some time saying a little prayer, to ask for protection, and surround yourself in white/golden light before a reading, its also good to imagine roots coming out of your feet and into the ground to centre and ground yourself also. I find this really helps, afterwards I would do another little prayer to remove all negative/ draining energies from you, and surround yourself in love and light x