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At present a visit to the ER is not required given the lack of any other symptoms like excessive lethargy, high fever etc.
The rash is likely to be an infected heat rash, and may respond to simple topical antibiotic application like Bacitracin / triple antibiotic cream.
However if the rash continues to increase, then a visit on Monday Morning to the pediatrician is indicated for confirming the diagnosis and starting oral antibiotics for the same as indicated,
The shots are unlikely to be related to these lesions as you are describing,Let me know if you need more information,