Q. If one already davened and is in a shul where they are davening, should one say over Ashrei or Shema if it's Tisha B'Av when we don't learn or say Tehillim?
A. In regard to reciting Tehilim on Tisha Beav, Mishna Berura (554: 7) quotes Magen Avraham that it is permitted after Chatzos. See similar in Halichos Shlomo (15: 8). See also Kovetz Halochos (20: 18) permitting when recited for the ill.
Horav Aharon Miller Shlit'a maintains that since these recitations are said in order to show togetherness with the Tzibur, they are also permitted.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit'a