Legal Question in Personal Injury in Illinois

In a word, yes.

Assuming the department store was responsible, they are liable for both special damages (your daughter's medical bills) and any general damages (like your daughter's pain and suffering).

The fact that Medicaid paid for your daughter's treatment is also not relevant to any settlement or recovery from the department store. What will likely happen is that Medicaid will assert a lien on whatever the department store or its insurer pays out. If a lawyer represents your daughter, a typical distribution is 1/3rd of the recovery goes to Medicaid, another 1/3rd goes to your attorney, and a remaining 1/3rd goes to the daughter.

I am not your attorney, and this is just general advice, but I might advise putting together some sort of demand letter to the department store and attaching useful exhibits like the pictures of your daughter's scar.