I am 28 and just had the rubella vaccine. Is it absolutely necessary that I get a second shot next month?

Maybe not. If the vaccine is required in your state to attend school, then to avoid a second rubella vaccine, blood can be drawn to see if immunity is already established from the first vaccine. If you live in one of the 20 states that allow conscientious objection for vaccines, then none are required.
Maybe, maybe not. A common misconception about mmr, or measles/mumps/rubella vaccine, is that the second dose is a booster. I reality, that dose is not a booster. But since 10% or more of all people may not respond to the first dose, we give everyone a second dose so more people respond. So, if you prove reactions all 3 parts with a blood draw, you don't need the second dose. But if negative, you need it.
Hard to say. They wouldn't have given it to you at your age unless you had shown no rubella immunity. Since you likely received an MMR in childhood, you are at risk of being a poor responder. If you want to risk having a baby that is deaf/dumb and blind or self aborts ignore the issue. Otherwise get the 2nd dose or have blood drawn to prove 1 is enough.