Just my 2 cents worth. I hope you and your 19month old get through this period of rash in good health. I don't have a whole lot to add as far as advice as to what to do, except one thing.
Upon reading your post, a question occured to me, actually, two questions, as I read your description of a mysterious horrible rash. #1 - it made me think back (at least try) and wonder about not only to the time of my own infancy, but to the infancy of people in general - all of us here, in wondering, at one point or another, didn't we all experience one or more various kinds of mysterious and horrible illnesses when we were infants, the same and similar kinds that may have caused our loving parents some stress and concern in the same way that you are experiencing right now? I'm thinking that yes, most of us probably did go through some similar "anxious moments". This leads me to ask - why?; why is your baby having such a horrible mysterious reaction to something, and as well, why did most of us as infants also go through periods of equally horrible and mysterious illness? All I'm trying to say is, there may be a bigger answer to be found here and your situation may be trying to help us to see it.
The #2 question that occured to me as it pertains to why is, does anyone else think this is likely and largely a matter that, just like most of us did when we were infants, your infant baby and her body may be going through a mysterious and horrible period as a result of her young body still trying to cope and adpat to what is probably a very routine, everyday, and "normal" thing she (just like and millions and millions of youngsters do and did) is being exposed to through collective environment to include diet? I don't say this to be mean, we've all been conditioned by what we accept and believe is "normal, everyday, routine 'good' food for diet". Maybe this mysterious and horrible rash is an outward sign from her little body - "hey, mom, dad, I love you guys, really, I do, but my teeny tiny little body was not really designed to tolerate the kinds of routine every-day diet stuff that it's getting..... and if it keeps on getting it, it may eventually adapt and "get over" this present rash.....but it may not, who's to say?". As I've gotten older, it's increasingly gotten established in my mind that all the various illnesses we all seem to "get over" in one point or another in our lives is likely more a matter that the illness is being encouraged to go deeper where it may then becomes less obvious and possibly dormant..... for a while, and this situation may even help us to become even more erroneously conditioned in using a common figure of speach "oh, see, we/she/he got over it, just like grandma said we would"
I guess another way of saying what I'm delicately trying to say is, perhaps your daughter's body is giving an outward sign that it's been getting something on a regular basis that it really is not designed for. What? Who knows, the possibilities are nearly endless..... dairy.....sugars (both real and fake).... fats (both real and fake)..... additives
in packaged/canned/jarred foods..... meat and or meat by-products......poisons from the local air, water and other environmental sources..... diapers and or diaper-substitutes..... lotions/powders/liquids/detergents/soaps/syrups/etc especially fabricated for youngsters.....hard to say. It may even be something she is not getting directly. Perhaps it is something that most of may initially think of as harmless or innocuous....something in the laundry detergent used, something sprinkled onto the carpet before it gets vacuumed, something sprayed into the air to "freshen" IE> change the odor that it has.... I dunno, it could be anything that is somehow becoming a routine every day part of your young daughters experience. Now may be the better time to try figurring out. Maybe in this way you can spare your daughter the experience of ending up like many of us old farts here, maybe today you can prevent her from ending up like us ..... in a health position to come to a web forum 10 to 20 to 30 years after the fact in seeking help for health problems that may possibly have been overlooked or steam-rolled over 10-20-30 years ago when we were all very young and first showing outward signs.
Good luck and hope you take this input in the spirit it was intended.