No, you can't "just start" birth control. I suppose when you say birth control, you are thinking of the birth control pill. Unless you've already been on the pill for one complete pill cycle and have been taking a pill every day, a BC pill won't do you a bit of good now. They must be taken one a day, every day, if they're going to be effective at preventing pregnancy. You have to go on the pill well in advance (usually one full pill cycle) before it is effective.
Anyway, if you're not already on the BC pill, how do you expect to be able to take one now?. Where are you going to get it? You have to see your doctor and get a prescription, and then take the prescription to the pharmacy and have it filled. If you've already got a prescription for birth control pills, why haven't you been taking them before now?