They gave two as Norocarp doesn't come in tablet form, only injectable. Rimadyl does the same thing but comes in a tablet form for the owner to continue the meds at home. So injection at the clinic and tablets to go home.
In response to the vet that said 'he must have picked up a virus from the RSPCA'. There is no way to prove he picked anything up from there. Thats a bit harsh, the dog could have picked anything up from anywhere, just like you and I do. The vet has given antibiotics as a precaution but without blood tests you cannot be sure if it is a virus. A blood test would show an increase in white cells.
The first vet was ok to give both injections (vacc & heartworm). The reaction rate is extremely low but you have to be aware that any drug can cause a reaction just like drugs with you and I. The first vet would not have been too concerned as reactions generally present themselves within 20 minutes of the injections. It is not unusual for a pet to be 'off colour' for 24-48 following a vaccination due to the immune system being compromised (better to compromise it for 48 hrs however than get Parvo where they will be vomiting blood and die a terrible death!). The first vet let you down with their follow up service and clear lack of patient care. As it was more than 3 days & your dog is still not well the vet should have looked at the dog, not the nurse. Being a nurse myself I would have expected the vet look at the animal in this case.
The drugs you got from your second vet are routine to cover all bases. Pain Relief and Antibiotics. Personally I'm not too keen on Welfare agencies with veterinary clinics, I've seen some hideous malpractice cases come from them. Just my opinion anyway but a private practice is always better in my eyes!