Hi Kim and good morning back to you.
I'm sorry that Miles Davis is having this issue. While most dogs tolerate vaccines quite well (like he has done in the past), I suppose it's possible that the Lepto vaccine that he received yesterday is responsible for the limping and soreness that he's experiencing today. I'm not usually a big fan of coincidence and it seems likely that this may be the culprit.
If that's the case, then he may benefit from anti-inflammatory medication such as Rimadyl or Deramaxx, etc. if you have any of these medications which your vet might have prescribed for him in the past. If you don't, it might be a good thing to call your vet and ask if they'd dispense a few day's worth.
Another option would be otc Aspirin as long as he's not vomiting. The dose would be 5-10 mgs per pound of body weight, twice a day with food to avoid stomach upset. This drug has anti inflammatory as well as anti pain properties.
Another option would be Acetaminophen which only has anti-pain properties. The dose would be 5-7 mgs per pound of body weight twice a day. Care should be taken if you have cats that they don't have access since this drug can be toxic for them.
If he's still limping after a day or so and/or if he stops eating or otherwise worsens, then a recheck with your vet would be a good idea; hopefully, though, he's back to his normal self fairly soon.
Hope this helps, as always, Deb