Well, most likely your symptoms are due to-Nerve compression.
It is too early to think about clogged artery .
The symptoms associated with Clogged neck artery are-
Feelings of dizziness, blurred vision and loss of vision in one eye signal the possibility of decreased blood flow to the brain from a clogged neck artery.
This seems to be case of Nerve compression or it can be muscle pull.
It may usually take 2-3 weeks for symptoms to get resolve.
Take Non-steroidal anti-inflammatory drugs such as ibuprofen.
You should Use ice packs to neck region for approximately 20 minutes, and repeat it every two hours. This can be done 3-4 times a day.
Take bed rest, and remain away from lifting any heavy objects.
In case the pain persist after 2 week, please see your doctor.They can advise for- X-ray of cervical spine, If required CT or MRI can be considered.Along with painkiller , your doctor can recommend Physical therapy.