It sounds like the Sanskrit words shiva and shrI put together, for which see
http://www.behindthename.com/bb/arcview.php?id=238910&board=gen and
http://www.behindthename.com/bb/arcview.php?id=736174&board=gen respectively. The -m- in the middle is grammatical. The construction shivamshrI, which would be from South India, would mean graceful Shiva.
Two points: I do not know if the word actually exists as a name; and I have no idea what ethnicity etc. the original person wanted. It would be nice if the page for new posts (as opposed to a response) reminded people to please put in as much information as they could.