The lower back pain in a 30 week pregnancy is something that might be expected. The position of the baby in the enlarged uterus puts additional weight on the back mucles which become tired and painful. Laying on your back might reduce the pain temporarily. Avoid unusual postures which might additionally tire the back muscles. Too much standing in one place or too much sitting might also increase the pain.
As for the vomiting, it might be the normal vomiting present during pregnancy. You might want to keep your self hydrated enough. You might want to consult with your gynecologist about which antiemetics you can use and are not harmful for the baby at the same time.
This all is if the back pain and the vomiting are not acute. If so, the lower back pain and the vomiting might indicate gastrointestinal problems. The back pain might also be related to renal conditions, like kidney inflammation or kidney stones.
You might want to visit an emergency service if the symptoms are acute and severe and are not relieved for a longer period (a couple of hours).
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