My 18 month old is teeth,would this cause a skin condition around her mouth?

My little girl of 18 months is teething her last big teeth.since starting teething she gets a spotty rash down below which only comes when she is cutting her teeth.She has a little at this stag but is going away slowly.she also has got a eczema type rash around her mouth, it hasn't spread at all since having it but it doesnt seem to want to go away.My guess is that its something to do with her teething otherwise it would of spread elsewhere.any advise?