Hello and Welcome, my name is Scott and I am an experienced small animal veterinary surgeon, I will be very pleased to work with you today and will try my best to answer your question to your satisfaction.
Sorry to hear about Millie's problem, so this happened today?
While there can be no guarantees I can tell you that serious injuries in this sort of situation with pups in Millie's age group are fairly rare, it would be more common for this to be something very much less serious such as a muscular strain or sprain.
Of course if the problem continues then you should have her checked over by your vet at the first opportunity but in many cases three or four days strict rest plus anti-inflammatory drugs and then a gradual return to exercise will resolve things if this is just a strain or sprain.
If your vet thinks this is a strain or sprain then he or she may prescribe a prescription anti-inflammatory drug but I know that some owners use aspirin in this sort of situation and report success. On a short term home remedy aspirin would be much safer and more effective than the other over the counter human pain killers and aspirin is sometimes prescribed for dogs. A typical dose rate would be 5 mg per pound of your dog's body weight twice daily. The judgment whether to dose with aspirin is of course up to you but here is a link to a an accurate web page with all the facts you might need including contraindications : LINK
I know your little Yorkie is very small but you may be able to split a junior aspirin.
" Is there anything I can do to encourage her to put weight on it " : Not really I am afraid, the way to go would be to just go for very strict rest, perhaps using something like a wire cat basket. Resting it as much as possible would encourage a bit of healing and then as I said a gradual return to exercise. A drug to reduce pain and inflammation will also help. Of course if something more serious is going on your vet will pick it up.
There is no way of saying at present if this is serious or not but in my experience most of these are minor injuries such as strains or sprains so the odds are with you. Common sense treatment such as I have outlined in any case will not make things worse if this does turn out to be something more serious ...
These things always happen over the Christmas period !
It is very encouraging that she is still trying to play ...
The bottom line is that many of these injuries will resolve with rest but if it does not start to improve after two three days rest or she gets worse in the meantime then you should have a vet check her over. Good luck, Scott.
Can I help you further Callum ?