The incidence of SIDA was declining per total of population before the back to sleep campaign due to better hygiene (lack of bacterial infection) increased breastfeeding, and better nutrition, better climate control for the baby, and not to smoke around a baby, or when the baby is in utero.
In real terms the incidence of SIDS has not dramatically reduced just because of the back to sleep campaign.
Research shows that babies put on their backs to sleep have slower development and gross motor skills associated with lack of sleep, as they have lighter sleep and never get the deep sleep pathways associated with proper brain development.
Some researchers recommend prone sleeping on clean ie. new) mattresses in a well ventilated room (even with a fan) without fluffy toys, bumpers etc as a way of reducing gastrointestinal problems such as colic and to reduce the incidence of scoliosis.
There are new studies showing that it's bacteria Staph a and E coli infestations that are a significant cause of SIDS, although they do say that it's easier to reduce the incidence of infection with supine (back) position.
Most pediatricians now recommend the back to sleep position, but in cases where the baby isn't getting enough sleep, if might be worth looking at a prone, or side lying position for the baby if she's just howling night and day, and not sleeping.
OP have a chat with your HV and your GP, and remember that all babies are put in a prone position in NICU... it's not the great evil that some posters on mumsnet paint it to be: there are many factory involved in SIDS, not just sleep position.
I suppose that if the baby has a lot of wind than she can be rubbed lying over a knee and left back to sleep.
Prone position sleeping, or side lying, with a new mould free mattress in a ventilated room without cot bumpers or teddies and without secondhand smoke, and not co sleeping with any other person - siblings included, may well be the answer for your problem.
Of course breastfeeding will reduce the chance of SIDS also - even one feed a day has been shown to have a very positive effect and alters the occurrence of SIDS quite significantly, by 50% in fact.
Check if the baby hasn't got an ear infection also: damage to the vestibular apparatus (the Eustachian tube etc) in the inner ear with infections or a traumatic birth (increased blood flow to the right ear from the placenta) may interfere with the respiration control when asleep.
Get her ears checked for infection. Though I have to say, it sounds like wind to me.
Good luck.