Petechiae

I took the kids to the pediatrician for a sinus infection and ringworm.  He was not concerned about the ringworm on the older child with the sinus infection, but when I showed him the ringworm on the younger child and inquired about the weird red spots in a strange pattern on her back he was concerned.  He said it was petechiae.  He checked her for fever, checked ears/throat for infection and asked about bruises.  She has several on her legs from soccer.  I told him she had fallen on the dog crate because her sister pushed her, and that is why she had one on her back.  2 weeks prior to the visit.  Plus they got ringworm from a inflatable jumping party place and she had played on those structures @ 2 weeks prior.  Plus jumped on a trampoline under supervision 4 days prior (no tricks, flips, etc.  did not land on her back).  He explained about low platelets and said to call if any other abnormal bruising occurs.  I started researching petechiae and I am very alarmed.  Why would he not order a blood test?  Should I request a blood test?  She now has more lighter red marks all over her back; however, we have used antifungal medicine on her for the ringworm.  He also gave us an antifungal shampoo to use to stop the ringworm from spreading to the hair.  She only has 1 patch of rw on the back of her neck.  The rash is varying color light to dark red and flat-tiny pinpoint dots.  The original spots are diagnosed as petechiae.  She is not taking any medications other than antifungal cream.  I did start her on a multi-vitamin again hoping she has some dietary deficiency rather than something horrible.  She does have asthma, but it is not causing a problem at this time.  She does not have to take a daily asthma medication anymore. Could the new spots be from the antifungal meds?