My guess would be that she is having a bit of separation anxiety. However, instead of showing it at her preschool, she shows it at home. One month is not really long enough to allow a child younger than 3 years to adjust completely to regular separations. It is important to be extra patient with her right now. She may want you to hold her all the time in order to be reassured that you aren't going to leave her. And, when you pick her up at school, make every effort to be punctual. In order to avoid your having to wait, the caregivers probably get her ready to go home a few minutes early. Then, if other children's parents arrive and you are still not there, she probably gets anxious. At her age she can't tell you about her anxiety; you have to read it from her other behavior. Chances are, if you give her time and a little extra support, this behavior will disappear before long.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.