When there is sudden neck flexure the cervical vertebra compress thre cartilidge. This often results in lifelong pain that develops six months to a year after the injury. There is disagreement on treatment.
You need an MRI.
Keep well hydrated, take NSAIDS.
One protocol is to use an axial traction device intermittantly (THREE TO SIX MINUTES) for short periods six to twelve times a day for the first three weeks. A cervical collar is often prescribed, but this is not a good idea except for the first day, because it encourages muscle atrophy and loss of muscle tone.
I would go to an ER of a teaching hospital where there is a neurologist and an MRI.
Well, it sounds like you pulled some muscles. I'm sure it's REALLY painful. I've hurt my neck and I feel like I'm dying. You many have a slight concussion, but really no treatment for that. Just be careful.
If your pain gets worse or persists, see a doctor. But a fall can really hurt because as you fall, your body tightens up in anticipation of the fall. That just endsmup hurting more muscles.