Welcome to the forum, Juliano.
Unfortunately, the sinuses don't have good blood flow and antibiotics don't work well. It takes several weeks at least to cure any infection. I hope you are under a doctor's care when using antibiotics. We're not doctors here, so we can't give you much advice on antibiotics and can only tell you what has worked for us.
I like a squeeze bottle which has a little pressure better than a simple neti pot which has no pressure. You may have to wash your sinuses twice a day for quite a long time to get relief. Also, the maxillary sinuses drain upward, which you find out after using a sinus wash and tip your head down.
If you have fall allergies or there is a lot of dust in the air right now where you live, that might be causing your sinus drainage. I see you have tried Zyrtec, but maybe a different allergy product might work for you. I'm taking montelukast right now. It's for asthma, and I don't have asthma, but it's helping me with my sinuses. It's a prescription pill, so you'd need to ask a doctor for it. Another thing, that is not prescription, is Mucinex Extended Release. I only use the 600 mg pill because the 1200 mg is too large for me to swallow. It's just guaifenesin, but that doesn't last long enough to do any good. The extended release formula helps me at night especially.
Try to ignore the thick mucus in the back of your throat as much as you can. It's hard to now swallow all the time, but that makes your throat muscles tired.
The teas you are trying do help some for a little while. I don't know about the vinegar or honey, but lemon and honey at least taste good in tea.
Best wishes, and it was nice talking to you. (I'm an old grandmother, so I like to hear from young people.)