Vaginal Candidiasis: This is the most likely diagnosis given the symptoms of white, thick vaginal discharge with a foul-smelling, non-fishy odor, and mild irritation on the inner labia minora. Candidiasis, commonly known as a yeast infection, is characterized by these symptoms and is a common condition in women.

Bacterial Vaginosis (BV): Although the discharge is described as non-fishy, BV should still be considered, especially if the odor is strong. However, the absence of a fishy odor and the presence of a white, thick discharge make this less likely than candidiasis.
Trichomoniasis: This sexually transmitted infection can cause a foul-smelling discharge, but it is often accompanied by other symptoms such as itching, burning, and sometimes bloody discharge, which are not all present in this case.
Vaginal Cytolytic Vaginosis: A less common condition that can cause a thick, white discharge with a strong odor, but it's less likely given the other symptoms.

Cervical or Endometrial Cancer: Although rare and unlikely given the symptoms, any abnormal vaginal discharge, especially if persistent or accompanied by other symptoms like pelvic pain or abnormal vaginal bleeding, warrants investigation to rule out malignancy.
Pelvic Inflammatory Disease (PID): This condition can cause a variety of symptoms including abnormal discharge, but it often presents with more severe symptoms such as pelvic pain and fever. It's crucial to consider PID due to its potential for serious complications.
Foreign Body (Retained Tampon or Contraceptive): Despite the question stating no foreign body, it's essential to consider this possibility, especially if symptoms persist or worsen, as a retained object can cause severe infections.

Desquamative Inflammatory Vaginitis (DIV): A rare condition characterized by a purulent vaginal discharge and significant inflammation of the vaginal walls. It's less likely given the description of the discharge as white and thick.
Vaginal Tuberculosis: A rare condition in many parts of the world, which can cause abnormal vaginal discharge among other symptoms. It would be considered in areas where TB is prevalent or in individuals with risk factors for TB.