Vaccines are used to build immunity to future infections. Giving a vaccine after catching the disease is too late.
Miles, Monroe, and Connor make a tactical error when they fail to gank Ed and the other patriot soldiers. By leaving Ed infected, they would have been better off leaving him in a pool with laser-equipped sharks. Ed is shown shortly after this receiving the antidote. Since Monroe planned to take on the patriots, ganking as many as possible would be beneficial to his cause.