Hi,
Thank you for posting your query.
I have noted your symptoms. Pain on eye movements are more likely due to 
optic neuritis, rather than a side effect of 
spinal tap.
Spinal tap may cause post-spinal 
headaches, which reduce on lying down.
For your pain on eye movements, you should visit your ophthalmologist. A course of 
steroids may be useful.
I hope my answer helps. Please get back if you have any follow up queries or if you require any additional information.
Wishing you good health,
Dr Sudhir Kumar MD (Internal Medicine), DM (Neurology)
Senior Consultant Neurologist
Apollo Hospitals, Hyderabad, India
Click on this link to ask me a DIRECT QUERY: http://bit.ly/Dr-Sudhir-kumar
My BLOG: http://bestneurodoctor.blogspot.in