@CJsBattle Good Job 
, Yes we can see the compression on the axial image (though some of them were bit blurry but I chose the one I thought was bit better in terms of visibility). We see the left hyoid horn (cyan arrow) resting against your left ECA (red arrow) anteriorly while the other right hyoid horn appears to be suspiciously touching the right ECA interiorly ( look at the different shapes of the ECAs, the left one appears to be oval perhaps induced by the compressing hyoid bone and the right one appears to be somewhat circular so might be touching but not compressing however provocative neck movements could change that). The ICA (yellow arrow) and the Jugular vein (blue arrow) appear to be normal and with no compressions. I think you need to investigate this further with competent ENT as some might ignore it. This could be why you are getting lightheadedness/presyncope.
BTW, I commend your skill in 3D slicer but I find a good quick tutorial that helped me when I joined this blog. You might need to tweak the intensity of the 3D image to remove the tissues and choose a bit clearer rendering so I put a link below to teach you that quickly so you can play around with it to produce more clear 3D images.
I think you can go to the volume rendering and play around with circled intensity bar to make it more visible and lessen the tissue. See the image below and you can read it the link below on how to do this if you need it.