Welcome in H.C.M.
I have gone through your query regarding painful and tender glands under lower jaw, and sides of neck along with thick veins on temple. You had also given your medical history .
After considering all about your symptoms it appears as most likely you are having sialoadenitis submandibular glands both sides with cervical lymphadenitis
As far as thick veins on temple are concern they are not likely to because of sinusitis
rather your hypertension
and increased lipid level in blood may be the possible factor.
Since you are already taking medicines for your other problems therefore you should investigate your submandibular region by ultrasonography
and FNAC to find out the disease concern, that will be accordingly manage.