Hmmm ... there are so many facets and differences in Islam beliefs that you might risk choosing the wrong one. Some the patterns - such as seen on the quilts of the Egyptian Tent Makers - seem innocuous enough but if you choose a design that is known to signify a specific Mosque, region, sect ... it might offend. I would certainly stay away from any of the designs that use words (and many do) - unless you had a translation and unless you knew that what it said would not offend (again ... it might be the wrong sect).
If I were you I would choose something that is a gift from YOU, something that signifies who YOU are - but at the same time will not offend. Something that you can both embrace. Some people are actually offended when someone not of their faith attempts to depict their faith.
The medical symbol is a good (and I think safe) choice, but you may not wish to applique. In that case ... perhaps a mariners compass or a lone star. Stars can have so many meanings to different peoples (most of them good) and different variations are usually looked upon as that - variations - with no ill consequences.