It sounds like you've strained those muscles, stretching them beyond their limit, or putting too much strain on them from a certain angle, or both. Something like push presses will recruit muscle fibers from the traps, as well as the neck to aid in the lift. And it's likely that you strained it, because if you'd torn something, you'd feel the difference. But only a medical assessment could tell you if you've got a strain or a tear, so don't take my word for it.
The best thing you can do for a muscle strain is to rest it, ice it, and use compression and elevation. I was one semester away from becoming an RN before I changed my mind to pursue a career in personal training, but I still retained what I learned while I was in nursing school! This is called the RICE method.
Don't do anything to overly exert those muscles for a while. This includes any lifting that recruits muscle fibers from those areas, or any other strenuous movements that might aggravate those areas. You can ice the muscles down, which will help reduce the pain and swelling, but make sure not to put ice directly to the skin. You can wrap a towel around the ice, or use another cool device (such as a freezer bag). You can ice the area down for up to 20 minutes, before you should take a break for about 20 minutes, and then you can ice again. In this case, you really can't use any compression method that I know of, due to the area of the strain. Usually they'll use some king of compression bandage if the strain is in an area where one can be applied. However, you can elevate your neck/upper back area by keeping it above the level of your heart. This will help to minimize swelling, which in turn will help reduce your pain.
If after a good amount of time off, you're still feeling a lot of pain, or sharp pains, then I'd recommend seeking medical attention. Or if the pain becomes very severe, or severe enough that you think you should see a doctor, then you probably should.
Just remember to rest up so you can heal well, so you can get back into the gym fresh and ready to go. Aggravating those muscles before they're healed could cause further injury, increasing the amount of time you'd have to deal with the pain and time off from the gym.
Hope you get to feeling better soon!
