I sustained a wrist injury 10 mos ago. I have a 6mm volar ganglion cyst and I continue 2 have wrist pain with my hand swelling. Would a shot help?

Need proper diagnosi. First you need a proper diagnosis as to why your wrist is still painful.Inyections may help to control wrist synovitis or inflamation but proper diagnosis is the key to a sussccelful treatment.
It may help . Reduce synovitis and swelling and discomfort but the end pint may not be resolution of the ganglion. Make sure that there is not a more severe injury such as an occult or unseen fracture or a major ligament injury as well. Since you cite 6mm ganglion it is likley you had an MRI but make sure it not a "red herring" ( tell your doctor that).