My ears hurt when I go to the bottom of a swimming pool or when I dive down snorkeling. Will that prevent me from becoming a scuba diver?

No, assuming you have no irregularities in your ears and sinuses. The discomfort is the normal effect of water pressure pressing in on your ear drums. Fortunately, our bodies are designed to adjust for pressure changes in our ears – you just need to learn how. If you have no difficulties adjusting to air pressure during flying, you'll probably experience no problem learning to adjust to water pressure while diving.