It's common for kids to go through separation anxiety at this age, and that may be what she's/you're experiencing. I would recommend that you do give her more reassurance, rather than less empathy.
Do keep your drop off short, sweet and upbeat, and develop a drop off routine... a special saying, handshake, a hug routine. Consider tucking in a picture of the family or of just the two of you in her backpack so she can look at it if she feels sad or worried. Think about arranging play dates so she can develop good friendships with classmates.See if another family member or friend can take turns with you dropping her off some days or picking up another friend on the way.
It's good that the teachers are involved and can take her from you at drop off. They see his over and over and should be well versed in handling it.
It is a phase that she's get over relatively quickly, so don't sweat it. Do remember that separation anxiety mean that there is a loving and strong bond between you and your daughter :) She's not putting on a show... she genuinely misses you~
Good luck~