Headache After Neck Lift and Blepharoplasty

The suture situation may be only inflammation and in my experience of over 22 years immediate suture rejection necessitating removal is rare.  The most likely cause for your headaches would be muscle contraction and spasm so if this does not resolve as you heal other causes may need to be investigated.
 

These answers are all excellent.
The stitch may need to be removed at this point.
Headaches have hundreds of causes and it is difficult to speculate as to the cause of yours. However, if I had to guess, I would attribute it to a tension headache due to pain induced positioning of your neck.
Although you can treat the headache, it would be best for you to treat the cause of the pain (the stitch) and then see if it resolves. If it does not, you may need ot seek a headache specialist.

The headaches can really be from all different sources.  A good exam may be the solution ot figure out the etiology. It could be from tightness and swelling, it could be from tension( stress) to name a few.  Really ahrd to say without an exam.

Headaches are not related to the previous surgery that you have had. The neck lift operation is tightening neck muscles, and there can be some tenderness and soreness in the neck for the first two weeks after the surgery.

The first thing I think of when you get night symptoms is swelling. At night, you lie flat and your head swells. The tightness from the surgery doesn't help much. The swelling makes everything a little more sore or painful. Hence the headaches.
To help your issues:
1. sleep in a recliner or on several pillows that supports your head, neck and shoulders.
2. Avoid salty or spicy foods.
3. Talk to your doctor to see if anything else can be done about the infection that appears to be resolving too slowly.