Hello stuzmate, and welcome to the spine forum.
As you may know, the medial branch ablation procedure, performed above and below C3, dissolves the nerves providing sensation to the facet joints, which are located at each level on either side of the dorsal or posterior spine.
These joints, along with the intervertebral disc, provide three-point stability with the that bears the weight of the spine at each level. These joints also allow us to bend, flex, and extend our neck and back.
Facet disease usually accompanies a complex of symptoms called spondylosis, and usually begins with degenerative disc disease (DDD), in your case, at level C3.
The joints become arthritic and painful. The RFA procedure is very effective in reducing this pain.
With cervical degenerative disc disease, the neck (and lower back) often lose their natural curvature, creating a state sometimes called "straight neck".
You are correct -- in this condition, your muscles are strained.
The Mackenzie exercises are often recommended for neck pain. Robin Mackenzie was a New Zealand physical therapist who wrote the books "Fix Your Own Neck" and "Fix Your Own Back". These exercises are good for releasing tension, and are not harmful in cases of mild to moderate DDD.
However, consultation with a licensed physical therapist can offer better suggestions more appropriate to your condition.
I used to enjoy massage with a therapist skilled in working the muscles of the neck. Yoga is also helpful, however, one must be careful with certain postures. No headstands, please!