Swollen tonsils can be caused by any kind of infection that causes inflammation of the tonsils (tonsillitis). The “large lump” on your daughter's throat is probably a swollen lymph node due to inflammation (lymphadenitis). Lymphadenitis is often a reaction to a primary infection in the tonsils. It is hard to say what kind of infection your daughter has but it's safe to say that she probably isn't experiencing infective mononucleosis (mono) because the tests for mono were negative. Several diagnostic procedures (blood analyses, microbiological smears from the throat) are necessary to identify the precise reason for a possible infection.
On the other hand, there could be some other more serious reasons for swollen lymph nodes and spleen-like tumors. A tumor is a less likely option than infection but must also be taken into consideration. You can request diagnostic tests with your daughter's pediatrician.