You can get damages for PSLA (pain, suffering and loss of amenity), but in the case of your DS, this is not likely to be a large amount where there is just superficial bruising, no scarring, no broken bones and no further treatment likely to be needed. It's very different for example if a child breaks a bone, because it means that there is a very high risk of arthritis later in life (for some broke bones, arthritis is almost inevitable). Therefore, it is unlikely that you would get a large amount (on his behalf). I would say under £1,000.
You don't mention any other incidental costs but these would be things like medical treatment, painkillers, physio, various therapies, time that parents have had to take off work etc. When you hear about multi-million pound settlements in the news, only a tiny fraction of that payment will be for PSLA- the rest will be for past and future losses. Unless you can quantify your losses, it will be difficult to succeed.
Also, there is the question of liability. If your STBX stepped out in front of a car that he presumably saw coming, I would guess that he will at least be held to have contributed to the accident. That would normally reduce any compensation by a percentage. There is also a chance that if there is no evidence of speeding, that your STBX will be held to be entirely to blame and the entire claim will fail (although in low value claims, the insurance company will often agree an out of court settlement).
The only way you can find out whether you have a case or not is to contact a personal injury solicitor who will take full details from you. It is likely to take some time to even get an idea of whether you have any prospects of success. The solicitor will need to know details of injuries plus all notes and records that the police made at the scene and evidence from the witnesses. It is only after all that evidence is available and has been analysed that you can get an idea of how strong the case is.