Is it permissible for me to travel again after I swore by "my divorce" that I would not travel, knowing that I do not remember the number of times I swore, and that I am now compelled to travel for trade? And do I owe an expiatory offering (kaffarah) for breaking an oath?

If by "by my divorce" one intends to swear by it, then it is an uncontracted oath. However, if one intends to swear by divorce in the form of a conditional oath (such as saying: "By my divorce, I will not travel"), then this falls under the ruling of conditional divorce. If the sworn-upon action is performed, divorce occurs according to the majority of scholars. Some scholars hold the view that if divorce was not intended, it does not occur, but an expiation for an oath becomes binding. The fatwa with us is in accordance with the opinion of the majority. Repeating an oath concerning the same matter is considered as a single oath. It is advised to be cautious of swearing by divorce because it is an innovated bid'ah.