I heard that on Shabbat one should not add personal requests to prayers; however I know of people who get together to say tehillim for cholim. We also daven for refuah in Shul. Is there an exception for cholim only or can one say tehillim and add personal requests?

In the Talmud Yerushalmi Shabbat 15:3, it states that one should not ask personal requests on Shabbat; nonetheless asking for the sick is not prohibited and is a common practice in all shules. This prohibition is manly for personal prayers which are not printed in the Siddur, added by the individual. Saying Tehilim dose not constitute personal prayers, the requests after the Tehilim should not normally be said, however if one feels sad by not saying them there might be a leniency to say them o Shabbat. (See Shulchan Aruch Harav OC 288:8; Ateret Paz 1 YD 2 branch 2 in length)