No. Do not bring snek

Why? You've literally just heard exactly why it is worse to do so. It doesn't help. It only hinders, and it means more people had to be put at risk. You are more likely to die by bringing the snake than by not bringing it. And either way you aren't very likely, so there is no need to take the risk, or delay going to the hospital longer to bring the snake which will delay you even more once you get to the hospital since the hospital doesn't need it and dealing with it costs time.

They don't know what snake it is by looking at it any more than you do. And even if you tell them what snake you think it is, they can't go by that. They will just run the test that tells them definitively anyway. Since getting it wrong is not worth saving the time or money of skipping that test. And while the hospital staff are heroes, they aren't the kind of heroes that want "relatively" secured snakes hanging around them. It will absolutely slow things down, not only for you, but for anyone else trying to receive timely care at that hospital. And that's best case scenario, it'll really slow things down if the snake manages to get out of whatever you caught it in. Keep in mind they are strong enough to open tupperware and while they are bad at getting out of bags, it isn't impossible for them to do so.