Two column proofs are the least-used type of proof in actual mathematics because the format is so very rigid. That rigidity is also why they're the first type we teach - it's much easier to teach something with specific rules, and it's much easier for a student to see what they're doing wrong when you can say "the reason you supplied was not 'given', a definition, a postulate or a theorem".
As to whether you are allowed to write a two-column proof instead of a paragraph, that's up to your teacher. What did she tell you? If no instructions were given, then it's up to you. Write it as you wish.
Writing a paragraph proof is in some senses easier than writing a two-column proof, but it's also harder to get it right. The overall idea is the same in all proofs: never make a statement without backing it up with solid reasoning. In a paragraph proof, you can occasionally relax the "always give a reason" rule, especially for things like givens and definitions, but it takes some time to learn where you can leave them out and where you can't. That's especially true because for every case of one person saying "that's obvious, you can leave it out", there will be at least one other person saying "it's not that obvious to ME". Judgment comes into play.
If you're going to write a paragraph, start by stating the facts as you know them. Draw whatever immediate conclusions you wish to from them, stating the reasons clearly, and continue on until you've proved what you want to prove. To quote Lewis Carroll in slightly different circumstances, "Begin at the beginning. Move on to the end. Then stop."