If she is starting to walk better day by day then most likely she just sprained it a little. Just give it some time. As long as it is getting better and not worse you probably don't need to take her to the vet.
My Cat Is Limping Since She Jumped Off The Top Of The Couch. Is It Possible She May Have Sprained Her Leg, Or Pulled A Muscle. She Is Walking Better Today Than Yesterday?
If you can afford to I say take the cat to the vet. Feel around and if she screams please take her