Could my child have diabetes?

I took my child to the doctor because he has been having several potty accidents So I thought he could have had a UTI which he didn't but the doctor still prescribed him antibiotics but told me that there was no sugar in his urine. There are several diabetics in my husbands family but my husband doesn;t have it. Also my son is only 3 years old and constantly pees now but it just started about a week ago. Could he get tested at such a young age? Should I wait until the antibiotics meds are finished?