Hi, Katherine. Here's the grim news:
The experts are all in agreement that no one ever goes to a psychiatrist complaining that they are feeling great and that they want it to stop. As you have found out, getting your brother to listen to reason is a non-starter.
Please don't give up. He may yet listen, but also know what you are up against, and don't blame yourself if you can't get through. In the meantime, watch him closely. If he keeps cycling up and his behavior gets more bizarre, you may be able to make a case that your brother poses a danger to himself and others. In which case, you may be able to compel your brother to be admitted to a hospital for a brief period of observation.
But that kind of situation generally needs to be extreme, and bipolars have a perverse way of acting calm and reasonable when the police show up. And hospitals are notorious for turning even raving maniacs loose. Moreover, dialing 911 prematurely risks alienating your brother forever. By all means, err on the side of a premature 911 call, but think very carefully.
Hopefully, your brother will settle down on his own accord, and the problem will go away. But there is likely to be a crash and burn. The crash and burn stage - either when cold reality sets in or he is depressed - is the best time to urge your brother to get help. In this stage, he is far more likely to listen.
In the meantime, look after yourself. This is a very stressful time for you. Your concern for your brother is apparent. But make sure you're talking to people who are concerned about you.
Hope this helps ...