Pyogenic Granuloma: This is a common condition that can occur over a pre-existing hemangioma, especially with a history of recent growth. The rapid growth over 2-3 months and the presence of a hemangioma underneath make pyogenic granuloma a likely diagnosis due to its known association with vascular lesions and its tendency for rapid growth.

Keratoacanthoma: Although less common, keratoacanthoma can grow rapidly and could potentially develop over a hemangioma. Its growth pattern and the fact that it can appear on any skin surface make it a consideration.
Seborrheic Keratosis or Other Benign Skin Growths: These are common skin lesions that can grow over various skin surfaces, including hemangiomas. Their benign nature and common occurrence make them a differential diagnosis.
Hemangioma with Superimposed Epidermal Hyperplasia: The skin overgrowth could simply be a reactive change over the hemangioma, especially if the hemangioma has undergone recent changes or if there has been irritation or trauma to the area.

Squamous Cell Carcinoma or Basal Cell Carcinoma: Although rare, the possibility of a malignant transformation or a malignancy arising in the setting of a long-standing hemangioma cannot be ignored. These diagnoses are critical to rule out due to their potential for serious consequences if missed.
Kaposi's Sarcoma: Especially in immunocompromised patients, Kaposi's sarcoma can present as a rapidly growing lesion over a vascular background, making it a critical diagnosis not to miss.

Metastatic Disease: Rarely, a metastatic lesion could present as a rapidly growing skin nodule over a hemangioma, especially in patients with a known history of cancer.
Angiosarcoma: A highly malignant tumor that can arise in the setting of a pre-existing hemangioma, making it a rare but critical diagnosis to consider.

Biopsy: Before any treatment, a biopsy of the skin overgrowth is essential to determine the exact nature of the lesion.
Electrocautery, Surgical Excision, or Laser Therapy: Depending on the diagnosis, these methods can be effective for removal. However, the choice of treatment should be guided by the biopsy results and the nature of the underlying hemangioma.
Conservative Management: For benign lesions, conservative management or observation might be appropriate, especially if the lesion is not causing symptoms or cosmetic concern.
Multidisciplinary Approach: In cases where malignancy is suspected or confirmed, a multidisciplinary approach involving dermatology, oncology, and possibly surgery or radiation oncology may be necessary.