There are two aspects to what you describe, and I'll address both separately and then together.
The first aspect is just feeling stimulated and energetic after Taiji practice. That's actually normal. This same stimulated feeling can happen when you're just interacting with a bunch of people socially. After the meeting, you just feel happy, alive, and energetic. You might be more talkative. Your mind will be racing with all kinds of thoughts. And you might feel that you need to move your body a lot more than normal.
This stimulated effect does wear off on its own. It can take some people hours to come down from this. If you're taking martial arts classes at night, it can actually cause you to lose sleep, because you feel so stimulated that you can't fall asleep at your regular time. I know that's true for me.
I hypothesize that what's actually happening physiologically is that your adrenal glands are more active and your brain is releasing a lot of dopamine. In other words, you're feeling stimulated.
Again, all of that is pretty normal. Most people will feel that way for some time after martial arts practice or even just any kind of positive social interaction.
The other aspect you mentioned is that you feel overwhelmed by negative, self-destructive, and depressed feelings after Taiji practice. And this disturbs you.
So here's the thing. Martial arts practice will evoke violent thoughts, even if they're only in the subconscious. That's just because you're doing things like punching and kicking. You're imagining a fight. And for some people, this can trigger negative psychological states.
There's a reason for your particular psychological reaction. You might not be aware of it, though. And I could only guess at it here. (Could be PTSD from being bullied or previous military experience, could be seeing your parents fight, could be due to being an HSP - highly sensitive personality, etc.)
To help figure it out, if it is something that concerns you (and it sounds like it does), you should consider making an appointment with a psychologist. A qualified psychologist can help you realize what's behind the negative thoughts and why they're triggered by martial arts practice.
The stimulated state is, I believe, combining with and amplifying the negative psychological reaction you're having.
One way you can come down off of the stimulated state faster is to do high intensity exercise after Taiji class. You want to get that excess energy out of your system. Exercise yourself to exhaustion. If you do it with high intensity, it might only take 10 to 30 minutes.
Try sprinting, jumping rope, punching a punching bag, doing burpees, etc.
Once you're exhausted, you'll probably find it easier to relax and fall asleep at night.
But that still doesn't address the negative psychological state you mentioned. Since you mentioned depression and self-destructive thoughts, I highly recommend seeing a psychologist who can figure out what the cause is. It could be an indication of something you never knew you had. If left to its own, other things in your life might trigger this, or it might become worse. This can result in manic outbursts that hurt you or others around you, emotionally and/or physically.
One other thing that occurred to me was that you mentioned you only experience the negative psychological state 5 minutes after class, not during class. This can have a number of explanations. Some are psychological, as I mentioned before. Some are neurological.
The neurological component may be due to a sudden drop-off of dopamine or other kinds of neurotransmitters after the class ends. So you're feeling high and then all of the sudden it goes away, and so now you're experiencing the rebound effect. This neurological effect has been known to trigger depression and self-destructive thoughts in people before. It almost sounds like a minor case of acute manic depression (bipolar disorder), but I'm definitely not qualified to make a diagnosis like that, so take what I say with a huge grain of salt.
So you might benefit from seeing a psychiatrist in addition to your psychologist. They can often prescribe medication to help regulate these sorts of things going on in the brain. If I were you, I'd first see a psychologist and talk about what's happening and ask if a psychiatrist might be a better choice for this issue.
Meanwhile, try the high intensity exercise trick I mentioned.
Hope that helps.