Does he enjoy the swimming part?
If so I agree with the poster above who said stop the lessons but find a local pool you can take him to just to enjoy the water and practice getting changed, using all the stuff like easy clothes for both of you, give them a snack while you get dressed (safely locked in a cubicle and with you standing in front of the door) etc.
It doesn't need to be presented or perceived as a punishment imo, just change it and if he asks why you aren't going to the old pool explain it wasn't safe for now but you might go again when he's a bit bigger.
I haven't got direct experience of ND kids but I do have two kids who were/are always the most boisterous in any group (middle is less so!) So I can empathise with feeling judged etc. And I can empathise with reaching a point where you're not sure at all what to do next to help your kid. I'm sorry, it's really hard.
Are there any activities where he is least likely to tantrum/meltdown? Or where he can last longest before it happens? I think if I were you I'd be doing those and trying to plan them to minimise a major problem. Eg short park trip, don't go near any equipment that frustrates him, snacks before journey home. Or whatever.
Maybe chat to nursery about your general concerns, they may have a staff member who could advise?
And don't blame yourself, honestly. You are doing the best you can, and so is he in his own way.