Hey L.: Not sure I understand your description of 'hot behind the neck'... Do you mean that your scalp is sweating at the base of your neck? Since I'm not sure I understand what you mean, this may not be useful... But my face/head always seem feverish when I have nausea. This might be something your body does in regard to morning sickness. Try one of those cold/frozen pads that you put in the freezer. Wrap a washcloth around it if it is too cold at first. Typically your local grocery store should have them for $9.
As for cold medicine... Sounds like you have a case of nasal drip. Maybe from allergies. Maybe because your sinuses and nasal tissues are changing (building more blood capilaries) so that they can pull more oxygen.. Its one of those things you body does when its pregnant however it can also make you more sensitive to sinus ailments/infections.
Truly, I would avoid taking *anything* over the counter during the first trimester. That's when the baby's development is most critical and sensitive to medications. Check with your doctor's office before taking anything (call the nurse if they doctor isn't available for phone questions).
However, in case this helps, here is a link to a site that says what you should avoid when sick and breastfeeding. I would think the same logic would apply to being pregnant...
Hope you feel better. (Again, put a call into the doc's office).