I put on Tefillin every day but tomorrow I have a funeral to go to in the afternoon. Do I put on before I go or is there a certain period of time that I do not put Tefillin on after the funeral. I do not know if this makes a difference, but the person who passed away is not Jewish and the funeral will be in a Catholic Church.

ב"ה Shalom, We have two issues here to deal with: One is exemption of a mourner of putting on Tefillin. When a Jew is a mourner for a relative who requires mourning, such as a parent, then the mourner does not put on Tefillin until after the burial because until the burial the Avel= mourner is busy with the burial of the deceased. After the burial, on the first of Shivah the mourner also does not put on Tefillin , however for a different reason. However, this does not apply when attending a funeral even for a Jewish person who is not a relative. Meaning if a person had planned to attend at a Jewish funeral for someone who is not a relative which would require him to sit Shiva there is no exemption from Tefillin whatsoever. The second issue is entering a church., which is forbidden according to Halacha. See: שו"ת "אגרות משה" יו"ד ג סי' קכט אות ,שו"ת "פרי שדה" ב סי' ד ,שו"ת "ציץ אליעזר" (יד סי' צא), All the best