Since this began after moving to a new house, I would suspect there might be mold or mildew, or even some other toxin affecting you. Headaches, sinus problems and chest problems are common with exposure to these things.
If you are renting, have your landlord do a check for these things. If it is there, they need to fix it at no cost to you. If you are buying and have recently just purchased, it should have been part of the inspection done on the house before you signed the paper work. Check with home owner insurance and see if they cover coming out to do a check on it.
There is not much else I can recommend to you except that if you can find yourself where there might be mold or mildew (usually gray or brown spots on carpet and walls from water being left there a long time), you can kill it by spraying Lysol, but a professional damage clean-up is best.
In the meantime, you may need to go stay with a friend or relative. If you are out of the house for a while and your symptoms get better, then you can be pretty sure it is something in the house.
Take care and let us know what you find out!