I doubt it's a question of lung capacity...more likely a question of how you're using your diaphragm and how you're controlling the air as you move it. For that, you need a professional voice teacher. Inexperienced singers often sing "too high" up in the throat instead of using their diaphragm effectively, and they also tend to expel too much air out of the mouth, thus losing their air supply rapidly.

Your voice will often sound breathy when you do the latter.

Shouting is extremely bad for your singing voice and can eventually ruin it. Whispering is also quite hard on the vocal chords, as is very lengthy talking. Singing, when properly done, does no harm to the vocal chords...but it's good to warm up first by doing some scales or other vocal exercises. It's unwise to sing "as loud as you possibly can", because that can eventually do damage too...better to sing up to about 90% of full possible volume, and let the microphone do the rest. Overusing any instrument will damage it, vocal chords included.

In short: Get a voice teacher. Any good voice teacher can teach you what you need to know in just a few lessons, and can monitor your progress.