Multinodular Goiter: This diagnosis is the most likely due to the presence of multiple nodules in the thyroid gland, heterogeneous echotexture, and mild increased size of the right lobe. The nodules' characteristics, such as smooth borders and mixed echogenicity, are also consistent with this diagnosis.

Thyroid Adenomas: The solid isoechoic nodule in the left lobe and the mixed nodule in the right lobe could be adenomas, which are common benign thyroid tumors.
Chronic Thyroiditis: The heterogeneous echotexture and mild increased size of the right lobe could also be indicative of chronic thyroiditis, an inflammatory condition of the thyroid gland.
Thyroid Hyperplasia: The presence of multiple nodules and heterogeneous echotexture could also suggest thyroid hyperplasia, a condition where the thyroid gland becomes overactive and forms multiple nodules.

Papillary Thyroid Carcinoma: Although the TI-RADS score is 3, indicating mild suspicion of malignancy, it is essential to consider papillary thyroid carcinoma, as it is a common type of thyroid cancer that can present with nodules and heterogeneous echotexture.
Medullary Thyroid Carcinoma: This rare type of thyroid cancer can also present with nodules and heterogeneous echotexture, and it is crucial to consider it in the differential diagnosis to avoid missing a potentially deadly condition.

Thyroid Lymphoma: This rare condition can present with heterogeneous echotexture and nodules, although it is less likely than other diagnoses.
Metastatic Disease to the Thyroid: Although rare, it is possible for cancer to metastasize to the thyroid gland, presenting with nodules and heterogeneous echotexture.
Thyroid Hemangioma: This rare benign tumor can present as a nodule with heterogeneous echotexture, although it is less likely than other diagnoses.