I fell and knocked my head yesterday, while on holiday. There was no bleeding or swelling and only mild soreness. Is it safe to fly home today?

It is safe to fly. You sound like you had mild head injury without any signs and symptoms of concussion. So, it is definitely safe to fly. Moreover, the airplanes have such good control of air pressure that even if you had a concussion, the danger with flying is minimal if not non-existent. However, because you just injured your head any expected side effects of flying such as jet lag maybe magnified in you.
I would watch for. symptoms of excessive or unprovoked sedation, confusion, sudden onset headache, blurred vision or pressure sensation, or profound vertigo or dizziness of sudden onset. Otherwise, you should be able to travel on airplane. Monitoring those symptoms are the most important aspect of surveillance for signs of head trauma.