I've recently started experiencing some seemingly involuntary head/neck movements. They are like small twitching or jerking motions. It seems to me like they may be related to a few possible causes:

Neck spasms, eye twitches or anxiety.

I've read that whiplash injuries can lead to neck spasms.

I've been doing vestibular eye exercises and I think that I may be noticing these involuntary movements the most after completing the exercises when my eyes feel a little bit "tired" or "stretched".

Another likely cause is that I've developed a kind of fear of movement. As a defense mechanism I think that I may be unconsciously stopping myself from doing some quicker head or neck movements out of a fear of reinjuring myself. This may lead to what feel like jerks or twitches as my muscles tense or stop me when I notice myself starting to move in certain ways.

It's hard for me to tell exactly what the cause is. Has anybody had a similar experience? I find it to be problematic because sometimes the movements lead to feelings of dizziness or nausea.

My opinion is it is due to number 4. You are overly anxious and trying to hold your head and neck still. This causes the nerves to misfire causing the twitching.

If I try to hold my hands still to do fine manual work like replace a battery in my wife's iPhone with its tiny screws, my hand(s) start to twitch.

There is no reason to be afraid of turning your head.

I think that this is related to my third point, which is probably the most likely candidate.

I think that at least part of it is that I'm unconsciously trying to hold my head still and that I'm reacting to movements that I start to make - especially bigger or faster movements.

I was probably trying to keep my head still, as you suggest, for a good deal of time and have ingrained some learned behaviours.

I don't think it's simply that I'm trying to hold my head still anymore - at least not on purpose - because I am now actively and consciously trying to undo these learned behaviours and force myself to move more naturally. These "twitching" movements often happen as I begin to move my neck, seemingly as an ingrained defense mechanism.

But sometimes there are small twitches that seem to come out of nowhere and I wonder if it's possible that these are related to the neck injury or perhaps just caused by anxiety in the body.

Number 3 would be right. I was count no 3 as the no 4.

More of an anxiety induced response due to your focus to move your head and neck smoothly. It is sort of like nystagmus except in your neck muscles rather than eye muscles.

That makes sense.

I've been struggling the last little while with quite a lot of symptoms and I was wondering what others do when they are overstimulated. I'm also curious if the vestibular therapy that I've started could be part of the reason for my increase in symptoms.

About 10 days ago I started doing some vestibular eye exercises that were prescribed by a vestibular therapist. I do three exercises:

I place a post-it note with a letter on it a meter or two in front of me. I keep my eyes on the letter and rotate my neck back and forth relatively quickly while keeping the letter crisp in my vision. I do both side to side and up and down for 30 seconds each with about 3 changes of direction per second.

In the second exercise I use two post-its and keep my head still while I quickly move my eyes back and forth between the notes. I do side to side and up and down for 20 seconds each.

The last exercise involves closing my eyes and turning my head to the side and attempting to bring it back to the starting point. I do left and right 10 times each.

I do a set of these three exercises three times a day and I think I'm starting to see some improvement in balance.

I've started having more headaches in the past week. I even have some headaches upon waking. Headaches have not been a particularly big issue for me before this point (although brain-pressure and brain-fatigue have been).
I've also had a lot of the brain pressure and fatigue. This symptom is usually the most indicative symptom of my having done too much mental activity, but I'm finding it coming on with less activity.

Some days I feel pretty overstimulated with many hours left in the day to go even though I'm pretty conservative in my activities. I'm trying to figure out what to do when most activities seem to exacerbate symptoms. I don't want to spend too much time sitting in the dark and potentially affecting my sleep as sleep has been a big issue for me. I also don't want to put strain on my symptoms when I'm feeling stimulated.

I would never be able to turn my head side to side 3 times a second. It would be too rough on my neck and cause other problems. I timed myself and I can do one head turn to one direction per second. I know that I cannot do it any faster. Just 10 turns in 10 seconds has caused my neck to tense up. The noise in my neck is quite noticeable. A headache is developing.

The up and down movement would also be rough on my neck.

There is no practical need to move your head any faster. Maybe you can do it at a slower rate for a while then build up to the faster rate.

If you want an enjoyable way to do the second exercise, try doing jig saw puzzles. They require a lot of back and forth and up and down eye movement as you look for pieces that fit. I do three jig saw puzzles a day at Jigsaw - MSN Games - Free Online Games
There are others that use larger puzzles on larger screens.
I use the edge and arrange functions as I do the puzzles.

I'm able to turn my head three times a second because the movements are relatively small - only about 20 degrees in each direction. The therapist says that for the purposes of getting the vestibular stuff back in order, the movements don't need to be big at all.

Jigsaw puzzles are a good idea, thanks.

For me, even 20 degrees at that speed is a struggle and noisy. Is your neck noisy?

But, I have had mild nystagmus in my left eye for decades.

My neck is noisy but I find that it's not noisy - or only mildly - at that 20 degree range.