Hugs, how exhausting and stressful for you all
My first impression reading what you've written is that there is something bothering her - pain or discomfort. I know how hideous it is when LOs wake every 45-60 minutes all night - but my experience with my own and on the boards here is that there is almost always something wrong when this happens - it's just that we haven't found it yet. The settling then crying again a few minutes later is typical of how my children behave when things aren't right. And it is very rarely 'just' a sleep training, routine or separation anxiety issue (though obviously these things can make it a bit more complicated).
Simple things first then - is she still symptomatic from her cold? Has anyone checked her ears? (pain often worse when lying down) Is she teething? Does she have any skin problems e.g. eczema causing her to itch or be uncomfortable? Is she too hot or cold at night? What about tummy troubles - gas/wind/unusual poos? Has she recently increased her solid intake or started new foods?
Have you tried giving pain meds - and if so, do they make any difference?
Hopefully we can help you get to the bottom of the problem. Hang in there x