Can a child have a bulls-eye bug-bite mark and have something else instead of lyme disease?

Anything is possible: But if the child has been in any area where there may be deer ticks they should be treated for lyme disease without waiting for serologic confirmation.

NO!!!: Nothing else is known to cause erythema migrans, the bulls-eye rash around a bug bite that is seen in up to half of those infected with lyme. If one has a bulls-eye rash see a doctor knowledgeable about lyme right away, as the sooner it is treated the better. See http://www.Lyme-disease-research-database.Com/lyme-disease-rash.Html.