There are several things that can be contributing to daily headaches after Lasik. We have more details in our article about Lasik Eye Strain
The dominant eye is the one that looks directly at an object (nondominant looks from the side at a slight angle). The dominant eye being myopic means that it is probably working overtime trying to focus on mid-range and distant objects. This alone can cause headaches.
Dry eye is most certainly a candidate for the cause of your headaches. That frequent of use indicates a rather severe dry eye problem, but it really sounds like you are using artificial tears to provide a temporary change in refractive error to compensate for the slight undercorrection. Yes, you can have dry eye, but the temporary good vision may be because of increased thickness in tears, not because your lack tears. You may find a contact lens reduces your use of artificial tears.
Your doctor can perform the tests necessary to determine to what extent dry eye is the direct issue. We have detailed articles about Lasik and dry eye
and dry eye treatment
that may be helpful.
Remember too that the tearing system is directly connected to the nasal and respitory system. If one has a problem, the other probably does too. Lasik can exacerbate other issues, so you may want to take a more general health perspective to the problems.
It is probably time for you to see your surgeon for an evaluation.