bed bug bites on baby's face????

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Uh if you have bed bugs I would say yeah. 
Get your house treated and get your baby away from them. Bed bugs can carry bacteria that could be harmful to babies.

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Could be, could also be mosquitoes from outside. Bed bugs usually bite in the form of a line or clusters. When it’s dark, turn the light on suddenly and lift his mattress/sheets and see if you see any

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Could also be a mark where they scratched themself? Has happened to us before where it started healing a little and looked kinda like circles instead of just lines... unless you have bed bugs - then definitely fix that.