I am sorry if this sounds simplistic, but you may as well rule out the simple things first.
Yous said that this has happened recently. Has she by any chance had some new shoes bought recently?
If children's shoes do not fit properly both in length and width, or have something in then such as a stone or lump or nail (if they still use them), or a buckle or strap that rubs, then somethimg as simple as that can cause a limp.
At age 3 she may not be able to tell you.