Can basal cell cancer increase my risk of melanoma?

Not per se: Both cancers are cause by exposure to uv light. Basal cell cancer by itself does not increase the risk of melanoma.

Indirectly: Basal cell skin cancers are almost always due to sun exposure. Sun exposure (and bad sun burns) increase risk of melanoma. If you are 29 and have had a basal cell, you should make sure you are getting regular screening examinations with your dermatologist on whatever schedule he/she sees fit. Biopsy of any suspicious lesions is important.

Yes: Having one type of skin cancer does increase your risk for develop another. You should limit your exposure to uv radiation and wear sunscreen on a regular basis. In addition you should see your friendly dermatologist on a regular basis.