Symptoms LPR or eagle?

They’re not the longest styloids we’ve seen on here but the are certainly longer than the ‘average’ , and the angle can cause symptoms too. As @Isaiah_40_31 says, you certainly have common symptoms of ES…
I’m afraid I can’t label the images for you, but as well as the styloids being long, your hyoid bone processes are quite long too, & the right looks like it’s got quite an upward curve- hyoid bone syndrome & ES symptoms are very similar, the choking sensations can happen with both.
It also looks like you’ve lost your neck’s natural curve, aka military neck, which we see quite alot. It can sometimes be the body’s way of compensating for ES symptoms by adjusting the neck, or it can be that poor posture, looking at screens alot have straightened your neck. There’s info & suggested exercises which can improve the curve in this discussion:
List of my favourite resources on YouTube to learn anatomy - General - Living with Eagle
It also looks like your IJVs are flattened a bit in a couple of places- slightly around the C1 process between it & the styloid, & a bit further down possibly by soft tissue, muscles maybe. But if you’re not getting any vascular symptoms (like head or ear pressure/ fullness, dizziness, off-balance feeling, pulsatile tinnitus for example) then your body is probably coping okay- it’s not severe compression like we often see.
Have you tried any nerve pain meds at all? They can often be helpful…
And what are your next steps, are you going to try and see one of the doctors on the list?