You probably need a Vet or Farrier or some other knowledgeable person if this does not resolve quickly. Shoulders and feet usually are the culprits when you have a lameness that is decidedly worse going one direction.
Checking hooves is best done using hoof testers. You will probably need a Vet or Farrier for that.
Then, every other part of the horse's leg can be checked with manual palpation and flexion tests.
When testing a horse's leg, always check the horse's good leg first. You have to have something to compare it to. Some horses are more 'flinchy' and less tolerant that others, so you need to know what to expect.
You check a shoulder by folding up the front foot with the hoof at the horse's elbow and then lift the folded up leg as high as you can in front of it. Then, keeping the leg folded up but back under it, lift it out to the side. The shoulder does not hinge that way and it is a frequent source of pain if the horse slips or lets its leg go out to the side. You will find that sore spot instantly when you try to pull his leg out to the side.
You can go through every other joint on a horse by methodically examining every joint.
The other thing you can do is check for her very early in the morning. Check for heat in the feet and then work your way up. Once a horse has moved around, their legs and feet warm up. Early in the morning, they should be cold as ice.