It's hard to be sure without seeing you, but it sounds like you tense your neck muscles as soon as you start kicking.
The basic TI sequence for backstroke is:
- back balance: Lean back in the water with your arms relaxed at your sides and your hands against your thighs. Let the water come up to the sides of your goggles and your chin, tilt your chin a bit toward your chest, and feel your abdomen rise to the surface. Do only a gentle kick. If you're doing this correctly, you should be so relaxed that you feel like you could go to sleep.
- head lead sweet spot: From back balance, rotate your body (but not your head) just enough that a bit of arm is showing from your shoulder down to your wrist. You will feel your gentle kick change from up and down to being partially sideways. The commonest errors people make on this one are (1) rotating their head (your nose should stay pointed up, even though your body is rotating), and (2) rotating too much (rotate just enough to show a bit of arm). Try this on both sides.
- hand lead sweet spot: From head lead sweet spot, slip your lower arm (the one that is completely underwater) up so that it is beside your ear, with your palm facing up. Try this on both sides.
- one-arm backstroke: Starting at head lead sweet spot, raise your upper arm (the one that is partially showing above the water) and bring it up beside your ear, rotating your body as you do this so that you end in your hand lead sweet spot on the other side (i.e., if you started in head lead sweet spot with a bit of your left arm showing above the water, you should raise your left arm and end in hand lead sweet spot with your left arm beside your ear and a bit of your right arm showing above the water). Then return to hand lead sweet spot on your original side, bringing the arm that is beside your ear under the water as you rotate your body. During the first part of the stroke, think about doing an arm wrestling movement with your stroking arm, but during the second part, think about throwing water toward your feet. As with the preceding drills, try this on both sides.
- two-arm backstroke: Same as one-arm backstroke, except that you combine the two movements, raising the arm at your side over the water as you stroke under the water with the other. Your core body rotation should be the driving force for both arm movements, and as with freestyle, you should think about railroad tracks, so that each lead arm and hand are in line with your shoulder on that side - not with the top of your head.
In all these drills, you should focus on being balanced and relaxed, keeping your abdomen at the surface, keeping your nose pointed straight up, and having a relaxed head.