3 1/2 year old Son has started gagging and making himself sick!

Hi ya everyone,  i've never done this before but not sure who to ask!

My son (3.5 years old) recently got diagnosed Autistic and we are just in the process of sorting bits out for him BUT in the last year he has started with a new "thing"!!

Whenever he gets really upset he start making himself gag and be sick.  Also when he gets a cough he does it as well! 

Now i have read on the internet that this may be a sign of SPD.  My son is also an extreme tippy toe walker( currently having neuro plates made but with little hope), picky eater and routine mad.

Im not sure how to handle this sick business and need some advise if possible.  Obviously mine and hubby's initial reaction was to tell him off as it comes accross as he's being naughty but then i thought maybe this and his autism may be connected and if it is then having a go at him wont work.

Im really hoping that someone out there can advise whether you are a doctor or in the health care sector or a mummy/daddy that has been through this as all these new little "things" are starting to worry me. 

Many Many Thanks

Mummy to my perfect boy