High cholesterol and pain in left neck right where carotid artery is. could it be blocked?

Very Unlikely: While artery disease typically starts ~age 7, at age 30 closed carotid is still very unlikely. Plaque rupture ; clots produce stroke with loss of brain function ; paralysis on opposite side of body, not pain. Cholesterol, in every animal cell membrane ; made by all human cells, has never been the correct issue. Get an “nmr particle test” ; go for excellence, LDL ≤700 nmol/l, large HDL ≥9 µmol/l.

Unlikely: Carotid artery disease in a young woman is highly unlikely regardless of the cholesterol level, and doesn't cause pain when obstructed. The symptoms of a blocked carotid artery is a TIA or stroke. There are a few rare conditions that cause carotid dissection in young women, but rare.

Unlikely: Carotid artery blockages, of any degree, do not cause neck pain. Blockages of the carotid can cause stroke or mini-stroke (transient ischemic attack, or tia). While carotid blockages from cholesterol plaque is unlikely in your case, you are within the age group for fibromuscular dysplasia. This does not cause pain but can cause stroke or tia. See a board certified vascular surgeon.

Carotid pain: May be something called carotidynia. Your doctor can check to see if you have inflammation. May need mri.