Your intention to brush up first aid skills is an excellent idea. Unfortunately, the system in the USA is not geared to doing a good job of teaching these kinds of skills.

You will probably find that the Red Cross class actually involves 90% instruction on CPR, and 10% instruction on first aid. Too bad, since the text they actually have on First Aid is quite a good book. In reality, their whole class should be turned around. They should focus 90% on first aid, and 10% on CPR. Except for special circumstances, CPR is often not going to be effective on people who have lost their pulse and breathing (exceptions being drowning, electrocution, choking incidents, and maybe de-fib [which requires a defibrillator and isn't taught in the intro class). So in other words, the curriculum doesn't really make sense.

Next step up is EMT training. This is definitely better in terms of taking more time to teach anatomy, illnesses, wounds, patient assessment etc. However, the whole EMT thing is also not really designed to make you an effective first aid provider. That's because the US medical system doesn't want you practicing medicine, even if it's just first aid. So the EMT course winds up teaching you how to get ready to throw somebody in an ambulance. My wife's joke - while I was taking various EMT classes - is that the correct answer to any problem boiled down to ... "oxygen and transport".

It's more likely that the military teaches effective first aid. They have to. And probably a number of other countries around the world havemuch better first aid classes than America does. Check for first aid manuals from places like Israel, Switzerland, Cuba etc.

Good luck.
It shouldn't have to be this hard.

Pete2