I do sympathise - my eldest dd also had night terrors, from about 2yo. Blood-curdling screams in the middle of the night, usually about 4hrs after she went to bed. Sometimes she went through phases when it was several times a night, and at other times, it went down to one every few weeks, but it was on and off until she was about 4.5yo.
She is also asthmatic, and the nightly coughs didn't help with the disrupted sleep pattern.
The biggest trigger though, was over-tiredness, feeling run-down. She had full days at nursery for 3 days a week, while I worked, and I noticed she would nearly always have a night terror after the third nursery day. From that, we knew over-tiredness was a major trigger...so tried to keep it at bay as far as possible.
We went to the Drs and was told that even though it was difficult, it was still 'within the range of normal', and that she would most likely grow out of it. She did, I'm glad to say - although it happened very gradually.
Things that helped:
Ventolin and clenil for the asthma
Antihistamine for hayfever/sneezing/itchy nose at night ('Allerief' - chlorphenamine maleate). Just thinking if your ds is rubbing his nose, perhaps it's itchiness from allergies. My dd rubs her nose too, but the antihistamine helps a lot. Or, if you don't fancy meds, try HayMax.
Naps if needed. If she got 12hrs sleep in 24, it was less likely (but still no guarantee).
Re. behaviour - again, over-tiredness had a very detrimental effect, but I did find the 3-4yr age to be a challenging, 'testing' phase anyway!
We had a difficult few months where she seemed very moody, wouldn't speak to me when she got home. I found the 'naughty step' didn't help after a certain point - and actually even sometimes made things worse. One appalling night she kept snatching toys off her baby sister, was placed on the naughty step, refused to stay on it, and almost kicked our (glass) living room door in, screaming. It was awful. She was tantruming, I was furious...
I stopped using it, and started using stickers and rewards instead and that worked better, to change what was fast becoming a rather negative cycle. Had to start off really easy though - so she was almost guaranteed not to fail - then worked in stuff like a star for every peaceful night, 10 stars and she got a treat. It didn't stop the night terrors, but it did lessen the frequency a bit, and started to move it in the right direction. Which suggests that some of it had become habitual, or behavioural (but not all).
Otherwise...there wasn't an awful lot we did that worked totally. In the end I think she just finally grew out of it, rather than any specific thing. Sorry, haven't got an easy answer!
On the plus side, she sleeps beautifully now (6yrs old), right through, all night - and is a happy, well-behaved, affectionate, cheerful, lovely little girl.
Good luck OP and hopefully sweet dreams in the not too distand future.