What Causes Persistent Headache?
Sinusitis most likely
Detailed Answer:
I read your question carefully and I understand your concern.
Regarding those diagnoses that you mention....cluster headache is a pretty recognizable disorder, it consists of attacks of excruciating stabbings or lancinating like pain, accompanied by lacrimation, stuffed nose, ptosis etc. These attacks last 5-180 mins. It doesn't seem to reflect your persistent pain.
As for the aneurysm, you should know that aneurysms themselves do not cause any pain generally. It is only when they rupture, with acute bleeding in the brain, that there is sudden onset, very intense headache out of the blue, commonly called thunderclap headache. So that type of headache doesn't seem to correspond to a ruptured aneurysm either.
Your other fear, brain tumor. The pain is of a gradual, progressive onset over weeks, with nausea and vomiting. However it is usually accompanied by other signs such as weakness or loss of sensitivity on the limbs on the other side, changes in behavior, seizures, it is rare for the headache to be an isolated manifestation. Also you mention tenderness on touch which is not typical for brain tumor at all, the brain is separated by the surface by the thick skull and superficial pressure doesn't affect it (that argument applies to the aneurysm rupture bleed as well). So while I can't technically exclude brain tumor I don't consider it likely at all.
Reading at your description I believe sinusitis to be the cause, the location, soreness and tenderness to touch are typical for it. I do not know how many days since you've started the prescribed treatment but sinusitis can take some time to resolve, a couple of weeks, even if the infection is responsive to antibiotics it takes some time for the sinuses to drain. Also some patients with recurring sinus issues like you may go on to develop chronic sinusitis which is hard to treat.
If the symptoms persist for several weeks head imaging would be advised, but (while it would serve to exclude that as well) not with brain tumor as primary suspect, but to view also the status of the sinuses and nasal pathways and for possible causes favoring chronic sinusitis.
I remain at your disposal for other questions.