Brief Answer:
CT/MRI scan of neck spine is required.
Detailed Answer:
Hi there,
Thanks for your query.
YES. You can take both medications together.
Neck pain and backache may be due to either, disc herniation/narrowing of 
spinal canal causing compression over the nerves; or, spasm of the muscles of back and neck following repeated coughing due to 
bronchitis.
If CT/MRI scan rules out the defect of the neck spine, a short course of anti-inflammatory drug + a 
muscle relaxant will relieve you of the pain. Addition of a muscle relaxant, such as, Tramadol or 
Chlorzoxazone, AND paractamol to ibuprofen should help.
A cough suppressant will enable the affected muscles time to relax and heal.
	
Consult your doctor and apprise him of my opinion. I am certain that he will agree  with my opinion;  order required tests, and- based on the reports-  will arrive at a certain diagnosis and  prescribe suitable treatment as advised.
Hope I have addressed to your concerns to your complete satisfaction and you find my response helpful and informative. I will be happy to answer further queries, if any.
Fond regards and have a nice day,
Col (Dr.) Rakesh Karanwal