Is it permissible to cry on Shabbos? What about if it is tears of joy? What are some halachos that pertain to crying (on Shabbos)? For example, can I tell someone something that may make them cry? What if I am sad, am I not allowed to cry? If I trip down stairs and I really hurt myself is it forbidden for me to cry? Sources please. Any answer will do but the more details the better.
The answer is yes.
As @Fred pointed in his comment, poskim addressed your question in SA OC 288, 2, I just want to show the Baer Heytev in name of the Taz:
(ב) הצער מלבו: וט"ז כתב דוקא מחמת רוב דבקות בהקב"ה מותר לבכות וכ"ה מצוי במתפללים בכוונה אבל כדי שיצא הצער מלבו לא ע"ש (ובאליהו רבה התיר).
The Taz allowed to cry because of great attachment (to G-d), this phenomenon is current in persons who pray with concentration and feeling. But to cry to purge emotional pain is prohibited.