I'm not in a religious school and can't wear my kipa there; but, I would like to wear my tzitzit (tallit katan). Is it permitted to wear tzitzit (tallit katan) without wearing a kipa?
Tsitsit is a Mitsva written in the Torah for men wearing some clothes fulfilling conditions of form and composition. Kippa is a custom linked to good character and humility. Both are excellent. As you can place Tefilin without Tsitsit and Brit milah without Tefilin, the lack of Kippa does not prevent the Mitsvat Tsitsit. It is obvious. Maybe I will add later some Chazal quotes.
Gemara Kiddushin 31b:
Rav Huna son of Rav Joshua would not walk four cubits bareheaded, saying: The Shechinah is above my head.
In Gemara this is presented as an great compliment about a great Chacham, as humility.
Shulchan Aruch Orach Chayim 2, 6:
אָסוּר לֵילֵךְ בְּקוֹמָה זְקוּפָה וְלֹא יֵלֵךְ ד' אַמּוֹת בְּגִלּוּי הָרֹאשׁ: :
This is prohibited to walking head up, They do not walk 4 cubits bare-headed.
Nowaday Kippa has a great signification as the famous "ערקבא דמסאנא" (shoe strap; According to Rashi Jews where tying shoelaces differently, not because Mitsva but because modesty, other commentaries says that the color of laces was different). So Bish'at Hashmad may be Yehareg veAl yaavor not least, if no more, than Tsitsit Katan.
According to some, you have to wear a Kippah outside in Public, but according to others less strict you only wear a kippah during prayers. The reason why we wear a kippah is because it reminds us of the Shechina and its bacially showing respect to HaShem. Also it shows that (when out in public) you are Jewish. I am just like you buddy, I wear kippah most of the time at school, and always wear tzitzit.But Boruch HaShem that I am going to yeshiva next year. I pray that you do to.