Iron Deficiency Anemia: This is the most likely diagnosis given the patient's low iron level (35 mcg/dL), high TIBC (510 mcg/dL), low iron saturation (7%), and low ferritin (7). These laboratory findings are consistent with iron deficiency anemia, which can cause menstrual irregularity due to the lack of sufficient iron for normal bodily functions, including hormone regulation.

Anemia of Chronic Disease: Although less likely than iron deficiency anemia given the high TIBC, anemia of chronic disease could be considered, especially if there are underlying chronic conditions. However, the ferritin level is low, which is more indicative of iron deficiency than anemia of chronic disease, where ferritin is often elevated.
Thyroid Dysfunction: Menstrual irregularity can be associated with thyroid dysfunction. Hypothyroidism, in particular, can lead to menstrual abnormalities and may also affect iron metabolism, though it's less directly linked to the specific iron study abnormalities presented.
Pituitary or Ovarian Dysfunction: These conditions can cause menstrual irregularity but would not directly explain the abnormal iron studies. Further evaluation of hormone levels (e.g., FSH, LH, prolactin) would be necessary to consider these diagnoses.

Celiac Disease: This condition can lead to iron deficiency anemia due to malabsorption and can also cause menstrual irregularities. It's crucial to consider celiac disease as it may not be immediately apparent but can have significant health implications if left untreated.
Gastrointestinal Bleeding: A source of chronic blood loss could explain the iron deficiency anemia. Although the patient's presentation does not directly suggest gastrointestinal bleeding, it's a critical diagnosis not to miss due to its potential severity and the need for prompt intervention.

Hemochromatosis (with Iron Deficiency): Although hemochromatosis typically presents with iron overload, rare cases might present with iron deficiency, especially in females due to menstrual blood loss. However, this would be unusual and not consistent with the high TIBC and low ferritin levels.
Transferrin Saturation Disorders: Disorders affecting transferrin (like atransferrinemia) are extremely rare and could potentially lead to abnormal iron studies. These conditions would require specific diagnostic tests and are unlikely given the patient's presentation.