I am sorry, but I have to wonder why you were allowed to grapple on your first day. Have you had training elsewhere? Noobs should not be doing grappling right off the bat.
About your neck. Go to a doctor.
About not putting ice on your neck, that is not right.
In fact, right after the injury you are supposed to put ice to reduce swelling and inflammation (within the the first few hours).
After that, contrast bathing is good (Alternating ice and heat every few minutes). This will create a pump like action to help flush out swelling.
After that, it is all about heat to encourage increased blood flow and relax the musculature.
Massages are NOT good during acute times, but are acceptable several days later when things are not so actue. And, furthermore, you should get it looked at by a doctor first to make sure it is not more than just a muscular injury. If there is skeletal or even a rupture in the disk, a massage therapist should not touch it for a while, or at the very least, should not do too much manual manipulation.
I am a licensed massage therapist and worked in rehab for many years.