In general, when one has a doubt as to whether or not he is obligated in reciting a beracha, the rule is that he should not recite it. However, Birkat HaTorah may be different, as the gemara[1] cites the pasuk, “When I call out HaShem’s Name, give greatness to our God,”[2] as the source for the obligation. Given the apparent Torah-level of Birkat HaTorah, most poskim[3] require reciting Birkat HaTorah when there is doubt.[4] Some prominent opinions[5] prefer that one not say Birkat HaTorah when he suspects he might have already recited it, due to the opinions that Birkat HaTorah is a Rabbinic obligation.[6] However, the accepted opinion is that if there is no other option, one does recite Birkat HaTorah in a case of doubt. In such a case, one should suffice with just the second beracha (“asher bachar banu”).[7]
In your case, however, there is reason to assume that you likely have already fulfilled the mitzva. The gemara[8] states that if one realized he did not recite Birkat HaTorah and it is now after davening, he is currently exempt from reciting the beracha, because he fulfilled the mitzva of Birkat HaTorah when he recited Ahava Rabba (the beracha before Kri’at Shema), which expresses our appreciation to HaShem for giving us the gift of Torah study. The gemara does not mention a need for special kavana in that beracha to thereby fulfill Birkat HaTorah. Thus, since you had completed davening, it would seem that you already fulfilled your obligation.
This is not entirely clear, however, as the Yerushalmi[9] states that Ahava Rabba fulfills the obligation only if one learned directly after Ahava Rabba. Some maintain that Kri’at Shema, which is words of Torah, counts for this, whereas others require that one say words of Torah that are not part of the davening, although these can be recited right after davening.[10] Unless you learned something not “davening-related” before you left shul,[11] your status would seem to depend on this unresolved machloket.[12]
There is likewise uncertainty regarding whether your wife’s beracha was helpful. The authorities agree that women are expected to recite Birkat HaTorah.[13] This is surprising considering that women are exempt from Torah study,[14] and Sephardi women do not recite a beracha on a mitzva in which they are not obligated.[15] The Beit Yosef[16] and Magen Avraham[17] explain that women must recite Birkat HaTorah because they are required to learn how to perform the many halachot that apply to them and because there are Torah passages in their davening. The Gra[18] posits that women are not obligated in Birkat HaTorah, as they lack the ordinary obligation to learn Torah, but they still may and are expected to recite the beracha for their voluntary mitzva. The Bi’ur Halacha[19] notes that one ramification of these disputing explanations is whether women can recite the beracha for men and thereby fulfill their obligation. According to the Gra’s approach, a woman’s voluntary beracha cannot count for an obligated man.[20] According to the Beit Yosef/Magen Avraham, however, women are able to recite the beracha on a man’s behalf, because women are also obligated in Birkat HaTorah. Whether your wife’s beracha helped you thus depends, once again, on a machloket.
Depending on the exact circumstances, there is another strong reason for leniency in your case. Your routine of recitations before arriving at shul, which you apparently did perform at least to some extent, includes Birkat HaTorah. In the case of someone who is not sure if he said the correct rain-related recitation in Shemoneh Esrei, we assume he followed his norm and said what he usually does (which depends on how long he has been reciting the current text).[21] This leads us to the working assumption that, unless we have strong enough reason to assume otherwise, you did recite Birkat HaTorah.
Furthermore, the Mishna Berura[22] rules that if a person’s doubt regarding whether he made a mistake arose only after davening is over, as opposed to close to the time of the possible mistake, he can assume he davened correctly. You began doubting yourself only after you went home, well after the omission might have taken place. Therefore, you may assume you did things properly (even if not with the usual level of concentration), unless you have a conviction to the contrary.
Putting all the indications together, you were not required to look for someone else to recite Birkat HaTorah on your behalf, and you certainly should not recite it now yourself.