Is what I did — a covenant with God to give 10% of what comes from the field of e-marketing — considered a vow that obliges me to fulfill it from any job or income related to computers, including the possibility of giving this percentage to my needy mother?

If your statement, "I will enter into a partnership with Allah," means that you will give 10% of your earnings from e-marketing as charity to the needy, then this is a vow (nadhr) that must be fulfilled. However, if you did not intend a vow but rather a promise to donate that percentage, then it is not considered a vow. Your obligation is discharged by donating that percentage from any amount you earn from e-marketing, whether you intended it as a vow or merely as charity. Passing thoughts have no effect; what matters is what you specified in your statement, which is e-marketing. It is permissible to give this percentage to your needy mother or to any needy relative, for close relatives have a greater right to kindness.