> I can still my thoughts for maybe one or two minutes before thoughts intrude and that makes me angry at myself at failing and I give up.

I recommend reading the book "Don't Shoot the Dog". It is about conditioning, but despite the book's name, most of the information applies to humans, too. It explains the details that matter, and how most people who try to use conditioning actually do it completely wrong.

One important insight is that using punishment to condition yourself almost always backfires. The reason is quite simple: every time you punish yourself for doing X, you are simultaneously conditioning yourself against two things: (1) doing X, and (2) noticing that you are doing X. If X is a bad habit, guess which one of these two things will be extinguished by conditioning first. And most people are already quite bad as self-understanding.

Therefore, perhaps the most important rule in meditation is to never punish yourself. (However, also don't punish yourself for breaking this rule. That would only mean breaking the rule twice.) Every time you punish yourself for "meditating incorrectly", you are going against what you are supposed to achieve by mediation. You are discouraging insight (to have made an error, that is a useful insight), and even discouraging meditation itself (the less you meditate, the fewer errors in meditation you can make).

In traditional Buddhist countries, beginners start with the loving-kindness meditation, and only later move to concentration exercises. Which is probably designed to avoid negative thoughts while practicing concentration. But many people in the West are likely to go straight to the concentration exercises, because they are looking forwards to increasing their productivity, and ignoring the loving-kindness meditation, because that's some stuff for hippies. And then they happily go and tell others to do the same. (Or course, a hippie who would only do the loving-kindness and never move on to concentration, would also be doing it wrong.)

The proper mindset for concentration meditation is unconditional self-love. You do it right, that's great! You do it wrong, hey, it's great that you noticed, and it's great that you keep trying regardless! Self-awareness and perseverance are wonderful traits, why would you ever punish yourself for having them?

Now the important thing is that you need to do this sincerely, not ironically (like, "I am such a loser, oh, good job noticing that, loser"). Self-deception would be the opposite of what you want to achieve. When I write that being self-aware (even of making mistakes) is preferable to not being self-aware (but making the same mistakes regardless), I totally mean it. But this attitude can be difficult to adopt, if you are not accustomed to having love expressed towards you (by others or by yourself). In that case, doing the loving-kindness meditation might help to overcome this obstacle.

I suppose that if you do meditation without punishing yourself, you will feel less exhausted. (Unless there are other reason, e.g. you were already exhausted, and mediation only helped you notice that better.)

tl;dr - to succeed at meditation, not being angry at yourself is more important than stopping your thoughts; you may want to train this skill separately