Does it persist? Sunburn has been shown to increase the risk of developing skin cancer many years later. Sunburn does not cause immediate cancer. Severe sunburn my require treatment by a physician or specialist. Was there was a skin lesion before the sunburn, or has it changed? Or if your skin does not heal or there is a persistent lesion, have it examined.
Your question? It is very unlikely that a skin cancer will immediately form at the site of a sunburn. Even if a skin cancer does occur after a sunburn, it generally takes years or even decades.