Sorry to tell you, but it's in your head. At least, not unless you also feel the radiation from your microwave oven...I remember thinkin' I felt my first X-ray, but I was freaking at the time. No to mention radiation rarely feels tingly, at least until after the warmth stage...remember I worked on nuclear warheads, and radio and microwave towers.
But you shouldn't feel an X-ray because even if you did feel it, it would be bouncing off your bone, causing that to "move", not your soft tissue. Not to mention the "heaviest X-rays" weight 4.04/(6.023x10^23) GRAMS. And a gram is 0.035 ounces, so if your calculator will do the math, it's much lighter than the weight of most of your individual atoms.
Remember, my mom's been doing X-rays since '84 so give me a call if you want to talk to her. She's highly intelligent. Does X-rays, CAT scans, Angiograms, MRIs, Ultrasounds, Mammograms, you name it.
