My mil had more than one fall towards the end of her life. We called an ambulance each time because after the first fall, when we weren't sure what she had done, the paramedics said elderly people who have fallen should not be lifted and moved, you should always call an ambulance. If they are able to get up alone that was fine.
Twice she ended up in hospital (the first time she had ever been in hospital in her 97 years) and a couple of times the paramedics checked her over, then moved her and checked again, stayed with her for a while and then gave her an all clear to stay at home. They were fab and they are the professionals so know what they are looking for.
As it happened, I was alone and unable to move her anyway due to my own ill health.
You wouldn't move someone at the scene of an accident, elderly people falling in their own home is no different.