How important is tummy time? my daughter is almost 3 months old and hates it! is it okay to let her scream for a few? are there any alternatives?

Not very: Tummy time is a way to help baby develop some muscle strength in the arms & upper body. Most who back sleep from the beginning are opposed to being on their belly & honestly i don't see why so much fuss is made over the issue. Early standards of motor development were developed when babies belly slept & haven't been updated since. Without tummy time some roll over a bit later. So what?

For ex-preemies & : Infants with developmental delays, it's very important for quality of movement as well as attainment of gross & fine motor milestones. . For a neurotypical, term infant, i'd try different textured mats & quilts on the floor, put large red or orange toys with faces in front of her, & lie down to make eye contact while smiling, talking & manipulating the toys for ~ 10 min at a time.