I get 300mg of Xolair injected twice a month (every 2 weeks). I was wondering if there are any studies showing long term side effects of this medicine that are not published by the manufacturers of the drug?
Yes, there are many studies, too numerous to list. I'm unsure of what is meant by "long term use", since the drug is relatively new.
For ethical reasons, it is required that every author state if there is a potential conflict of interest (e.g. the study was funded by the manufacturer.) Just look at the beginning or the end of the paper, where it lists if there is a potential conflict of interest. Look under "Author information" and "Grant support" sections; some even list it under "Disclosures" or other similar names.