That sounds so hard! Is she hungry? Or cold? How much sleep is she getting in the day? Apparently at 3-4 months is should be in the region of 3.5-4hours and too much day sleep could be effecting her night sleep. We have a similar issue at around 5am, no amount of feeding or settling her will work
Following as in the same situation except I can’t even put her down during the day. She wakes up after ten minutes.