This is a very good question, and you must first understand some general concepts about cancer and chemotherapy
before it can be answered. Cancer cells in a very basic sense are normal cells that have mutated or changed such that they lost the ability to regulate cell growth and cell death. The is a continuum of how much mutagenic change has taken place which compares the cancer cells a the state that they are in to "normal" cells. It makes sense then that the farther the cells are mutated from normal, the more "poorly differentiated" the cells are, and (typically) worse the cancer is.
Cancer cells then usually have a faster rate of growth and cell division then normal cells do. Most chemotherapeutic agents aim to cause damage to cells as they under division, or try to prevent division altogether. In so doing, they are somewhat selective for the cells that are dividing more frequently, which are mainly the cancer cells. Unfortunately no chemotherapy regimen is perfect, and while the purpose is to kill only the cancer cells, any normal cells that are multiplying rapidly can also be targeted (this is why with some chemotherapies there is hair loss...hair follicles multiply rapidly). Furthermore, the cellular contents of the cancer that are released when the cells die from the chemotherapy can cause a severe immune reaction resulting in very bad illness
. So the simple answer is that yes with certain chemotherapies, the patient can definitely get "sicker". If this is a personal question, I would definitely recommend discussing your concerns with your oncologist