Rheumatoid Nodule: This is the most likely diagnosis given the location over the metacarpals, the nodule's characteristics (immobile, nontender, irregular borders), and its migration proximally. Rheumatoid nodules are common in patients with rheumatoid arthritis and can appear over bony prominences, tendons, or joints.

Ganglion Cyst: Although typically more fluid-filled and fluctuant, a ganglion cyst could present as a firm nodule, especially if it has undergone degenerative changes. Its location over the metacarpals and initial appearance over the MCP joint of the 3rd digit are consistent with this diagnosis.
Tenosynovial Giant Cell Tumor (TGCT): Formerly known as giant cell tumor of the tendon sheath, TGCT can present as a firm, nodular mass adjacent to joints or tendons. It is usually slow-growing and can be asymptomatic or cause mild discomfort.
Lipoma: A lipoma could present as a subcutaneous nodule, but its typical characteristics include being mobile, soft, and having well-defined borders, which does not fully match the description provided.

Soft Tissue Sarcoma: Although rare, soft tissue sarcomas (e.g., liposarcoma, leiomyosarcoma) can present as subcutaneous nodules. They are critical to diagnose early due to their potential for aggressive behavior and metastasis. The irregular borders and proximal migration of the mass could raise suspicion for a malignant process.
Metastatic Disease: Metastases to the soft tissues from other primary cancers (e.g., lung, breast, melanoma) can present as subcutaneous nodules. Given the potential severity of metastatic disease, it is essential to consider this diagnosis, especially if there is a known history of cancer.

Amyloidosis: Cutaneous amyloidosis can manifest as nodular deposits in the skin, although this is less common. The presentation would be unusual for amyloidosis, which more typically involves systemic symptoms or other specific types of skin lesions.
Scleroderma Nodules: In the context of systemic sclerosis (scleroderma), subcutaneous nodules can occur, but they are less common and usually accompany other manifestations of the disease, such as skin thickening and joint involvement.