Welcome to the forum!
Stiffness in neck and eye pressure may not be due to allergies. The most common cause is compression of the spinal nerves in the cervical spine region. This can happen due to overuse of computers, work involving straining of neck, canal stenosis, bone disease, spondylosis, poor posture etc. It can cause dizziness and nausea.
This could also be due to associated ophthalmic migraine. The other possibility is ‘benign intracranial hypertension’(BIH). This happens due to impaired CSF absorption. A generalized throbbing headache worst felt in the morning and last thing at night. This headache is generally relieved on standing (consistent with raised intracranial pressure). This also causes visual defects.
It is difficult to determine the cause on net. Please consult your PCP to start with.
Hope this helps. Please let me know if there is any thing else and do keep me posted. Take care!
If it turns out to be compressed nerves your best bet is a good chiropractor. Swedish massage is also good.