The gemara[3] cites Rav’s statement that a non-Jew may not make tzitzit for a Jew. His source is the pasuk[4] that instructs us to make tzitzit, which addresses “the Sons of Israel,” excluding non-Jews. Tosafot[5] comments that this implies that women would be able to make kosher tzitzit, as only non-Jews are excluded, and this is indeed how the Shulchan Aruch[6] rules.
On the other hand, another gemara[7] derives from the p’sukim “You shall fasten … You shall write …”[8] that only those who must wear tefillin can write tefillin, mezuzot, and sifrei Torah, which excludes non-Jews, women, and children. Tosafot[9] cites Rabbeinu Tam’s view that this is part of a general rule that only those who are obligated in a mitzva can create the halachic object needed for the mitzva.[10] Therefore, Rabbeinu Tam maintains, tzitzit tied on to a garment by a woman are invalid. Tosafot disputes this view based on the aforementioned gemara and another gemara that validates a sukka made by a non-Jew, concluding that the halacha regarding tefillin, mezuzot, and sifrei Torah is unique because it results from a special derivation. The Rama,[11] however, cites the strict opinion and recommends being careful l’chatchila not to have a woman make tzitzit as well.
The Magen Avraham[12] suggests another reason why women should not make tzitzit – the term “the Sons of Israel” often excludes not only non-Jews, but also the “Daughters of Israel.”
The Pri Megadim[13] claims that the reason to exclude women from attaching tzitzit (if indeed they are excluded) is relevant to the status of minor males. If the reason that women may not tie tzitzit is that they are not obligated in the mitzva, the limitation applies to minor males as well, as they too are not obligated in tzitzit on the level of Torah law. In contrast, the limitation on “the Daughters of Israel” would not apply to minor males, as the mitzva of tzitzit was addressed to them as well, even if they are presently too young to be fully responsible for any mitzvot.
In any case, the Magen Avraham equates women and children in this matter, making the status of your tzitzit questionable. The Mishna Berura[14] says that it is proper to deter a katan from making tzitzit that are meant for a gadol (apparently only for Ashkenazim, as Sephardim follow the Shulchan Aruch’s view that women – and thus minors – may tie tzitzit). However, the Mishna Berura also writes[15] that once a katan made tzitzit for his own garment, when he becomes a gadol, the question of whether he may continue to use them is a question of b’di’eved, and he may therefore use them as is.
In this regard, however, a katan may lack one halachic requirement for making tzitzit that a woman possesses – the ability and reliability to do things properly without supervision. It is possible to check to see if the physical action that the katan executed was done properly. However, what about the required kavana[16] to create valid tzitzit? The gemara[17] writes that the threads of the tzitzit must be spun lishma (for the purpose of the mitzva). Although the Rambam[18] says lishma is not a requirement for attaching them to the garment, the Rosh maintains that the attaching must also be done lishma, and we try to follow the latter position.[19] Therefore, even regarding a b’di’eved situation, we can trust the katan to have attached the tzitzit with the proper kavana only if an adult was instructing him to do it lishma.[20]
In your case, however, the situation is significantly better. You do not have to convince someone else that you had proper intention. Rather, if you are confident that you had in mind that you were attaching and tying the strings to be used for the mitzva of tzitzit (which is highly likely), you can continue to use them.[21] If you are not confident that you had the right intention or if you want to follow stricter opinions than those that we presented,[22] you should undo the tzitzit fully so that the whole tzitzit will be formed properly.[23]