First of all, nobody here is qualified to diagnose you. You have seen doctors and need to do what they say as they are trained in medicine. Your doctor is indicating you have an infection and need follow up. Do this first. There are a million things it could be but only a select few it can be. You have been battling this all year and are asking strangers on the Internet what it is. I don't know what type of doctors you have seen but many of us have seen a dozen or so leading up to diagnosis. Do not stop with one until you know what is wrong. I would not worry about cancer till the conclusively tell you through pathology. Going out and asking for a fine needle biopsy probably won't work either.

By the way high monocytes are classic infection, parasites or chronic inflammation...never leukemia and rarely any indication of cancer. Your doctor wants to check titers to determine what viruses your body has created antibodies for or what you have been exposed to since monocytes indicate potential infection or more important viral infection. Listen to the doctor and take care of this. Infection this long is never good. I would list things it could be but your guess is as good as mine.

Try not to worry about every possibility and get back to the doctor immediately. The body cannot battle infection indefinitely. Chills and night sweats are your body fighting fever or sever inflammatory response. This is nothing to take lightly. If your doctor isn't moving fast enough, run to another one. This is your health and you need to take action.