If the white residue is only on her tongue and not on the insides of her cheeks, then it may only be milk residue and not Thrush which is a yeast infection of the mouth.
If you do suspect it is Thrush, then it may be painful for her to nurse or bottlefeed and you should take her to a doctor so that she can get a prescription for Nystatin.
Also, make sure you sterlize her pacificers/ bottle nipples....anything going into her mouth.
If you are breastfeeding and she does have Thrush you will have to be very careful so that she does not pass it to you...you will most likely have to put the Nystatin on your nipples.
The spitting up would not have anything to do with the Thrush, babies do spit up every now and again.....monitor it and see if it seems to be ongoing and often....then check with her doctor it is very often .
Here is more info on THRUSH: http://www.babycentre.co.uk/refcap/92.html