We had that with DS7 starting when he was about 2 1/2. It was a bad year for him (gained 3 ounces in the year, refused to go outside for fear an animal would bite him). He's a very anxious youngster, and we still have to watch out for the triggers. The beginning of the school year is one, so our house is SOOO fun right now!
I read the Asynchronous Child when DS was 4 or 5 -- very applicable to him. At 5, we spoke with a psychologist who observed DS anonymously in class and he pretty much wanted to go straight for meds. I wasn't on board with that for one so young, and we still try to find ways to help DS deal with his anxieties by talking them out.
One thing the psych said that I found valuable:
Excitement and anxiety are two sides of the same emotion. The mind responds to both the same way. So, it's not surprising when DS has the same issues (fear or acting out) both when excited and nervous. Not sure if you see this with your child, but for us it's something to be mindful of, so that we try to be supportive enough during those times.
DS and I have frequent conversations about how sometimes our minds (I am similarly anxious) mistakenly over-react to things, and how we need to be aware of that, and try to teach ourselves to question our reactions and see what really makes sense.
In times of "high stress", DS has almost no control over his emotions if he's tired or hungry. For example, we don't allow DS to play chess before breakfast or dinner, because he can't see it as a game when he's hungry. So, if his little brother (DS5) makes an illegal move or loses interest, DS7 goes completely bonkers. Our present approach is to continue to enforce our rules regardless of DS's level of anxiety, and to try not to let our frustration/anger show as we enforce them. During his anxious times, we also try to limit other triggers, but life can easily get in the way of that.
I wish you luck with your DS6. He's lucky to have a Mom who's observant and concerned.