I am sorry to hear that you are having such trouble with your sinuses! If you have not talked to your primary care doctor
about this issue, I would recommend that you start there. There are many prescription medications that are used to treat sinus congestion and the associated symptoms, and hopefully one of these will be of use to you.
It is likely that the burning sensation inside your nose is from irritation and inflammation of the lining of the nasal passages. Unfortunately, there is no great treatment for the burning sensation per se, other than general treatment for the nasal inflammation and sinus congestion. Improvement here should also improve the burning sensation.
Some of the medications that are typically used include anti histamine medications like loratidine (Claritin) or cetirizine (Zyrtec). In addition to these, nasal steroid sprays, like mometasone (Nasonex) or fluticasone (Flonase) are also very helpful. In some people, especially those with a significant component of congested and irritated nasal passages, irrigation of the nose with a saline spray can also be useful.
Start by seeing your doctor. They can confirm the diagnosis and help you get started on the right medications for your particular set of symptoms.