Put a heating pad on your neck. It will soothe your muscles too. Ice also has the same effect. Remember to keep moving it. Avoid any sudden movements. That could make your neck worse.
You could also use pain relievers. Over-the-counter medicines include ibuprofen and acetaminophen. Massage the area. Do it very lightly.
Turn your head the opposite direction of your pain. Since it hurts on the right side, turn it towards the left side.
I hope your neck starts feeling better.
Other than that, I hope your babysitting goes well! :)
take a break move to stretching and slowly work back into physically exercising if the problem continues go to a doctor or physical therapist