First of all, emergency measures. Well done for getting him into a seatbelt when he was melting down. A seatbelt is MILES better than nothing, even though it would be better for him to be in a car seat. And nothing happened. Please don't feel bad about this - you did the exact right thing.
Could you maybe get a high back (Maxi Cosi do a folding one) or backless booster to keep in the car, in case of another emergency? Again it is not ideal, and probably wouldn't recommend this as his main seat unless it turns out it is the only kind of seat he doesn't melt down in. But it would offer you an improvement over the seatbelt alone. Even a backless booster is a significant improvement - you can also slide the front seat as far back as it goes, to increase distance from the airbag, and consider turning it off if it's easy to do that - it's often a key turn in the glove box.
If you do end up driving him just in a booster or just in a seatbelt, it is probably safer to drive normally as you will be more predictable to other drivers. I understand why you went slowly, but it's probably not necessary - I would just try to get home by the most direct route so you're minimising time on the road when he's in a non ideal form of restraint.
In terms of forward facing options, you have a few.
25kg harness R44 seat - Joie Bold R, Cozy n Safe Hudson or Cozy n Safe Excalibur/Puggle Safe Fit & Grow - these can use the 5 point harness up to 25kg. Cost about £100-150 depending on model. Fits using isofix, seatbelt and top tether. Do note to avoid the R129 type versions because they are usually limited to 105cm on the harness, whereas the R44 ones have no height limit.
Special needs harness seat e.g. Britax Voyager - these have higher weight capacity, but are much more expensive i.e. over £1000. You might be able to get funding somehow - I would ask on the SEN boards because I'm not sure how this works, whether it's through Motability or something else.
Special needs harness like Crelling harness combined with high back booster. Less expensive, around £200 per harness and you can combine with any booster you like (I believe) so you could look at things like Britax or Besafe or Axkid. The In Car Safety Centre sell these and have an advice service and I am sure there are other services as well which offer advice on these. He would need to be over 15kg and 100cm I believe. The harness itself is mainly designed to keep them in the seatbelt, rather than restrain them for crash safety.
Cybex Anoris as pictured above - that has an impact shield, rather than 5 point harness, and the Anoris has an airbag inside the shield as well which should inflate during a crash which helps support the head and neck. The crash tests of this are seriously impressive, but it's not a cheap seat - about £500/600 depending on the version - and it is limited to 21kg/115cm so doesn't last as long as any of the other above options.
Possibly something like Besafe Beyond? This is a 23kg/125cm limit rotating seat. So it can be rear facing, like the Minikid, but could be turned FF if he is struggling and needs that on a particular day. The downside again is the lower weight limit and the cost of it - it's about £650 because you need the rotating base and the seat.
If child is over 100cm and 15kg and is close to 105cm/18kg - a decent high back booster might be worth a go. It's not an ideal car seat at age 3.5, especially if he doesn't have the understanding that he needs to sit still, not play with the seatbelt etc. But OTOH any properly fitting car seat for his height and weight which he remains in is MUCH better than no restraint at all and you have to weigh this up.
Personally if money was no object and he has enough growth space to make it viable, I'd try the Cybex Anoris or the Besafe Beyond, but I'd want to try the Anoris out in a store to see if he actually copes with the shield because some children would find this too much in a sensory sense.
So in a more practical sense I would most likely end up with one of the 25kg harness R44 seats, and hope that by the time he reaches 25kg, he has enough understanding to use a high back booster correctly. If not, then readdress the Crelling harness / SEN restraint question.
OTOH if you are certain already that you will end up needing the longer term option eventually, it might be worth opting for that straight away, since they are pricey so you might as well get your money's worth.