Because you were prevented from completing umrah that you had set out to do, you are advised to offer a sacrifice; but the sacrifice must be done in the haram. This is an inference from the following verse in the Qur’an:

“And complete the Hajj or ’umra in the service of God. But if ye are prevented (From completing it), send an offering for sacrifice, such as ye may find, and do not shave your heads until the offering reaches the place of sacrifice.” (Qur’an: 2: 196).

And since you are not able to do it by yourself as you are living abroad, you may delegate this task to someone going for umrah or hajj or living there. All that is required in this case is for you to send money to buy a goat or lamb as a sacrifice to be given to the poor in Makkah. If you contact the reputable organizers of hajj or umra, they would be able to help you, if you don’t have any other direct channels.

Having said this, I must also point out for your own knowledge the following piece of beneficial information:

Although the standard ruling in fiqh is that women who are menstruating cannot perform tawaf at all; however, there is another acceptable view on this held by scholars such as Taymiyya, and you would have been perfectly justified in following his ruling and thus you would have been able to perform umrah while still in menses because of your own special circumstances. As Imam Ibn Taymiyyah has rightly pointed out that it is permissible for women who are menstruating to complete tawaf, if they have no choice but to leave Makkah before the expiry of menses. You could have done so taking all due precautions. In that case, your umrah would have been considered as valid. Ibn Taymiyyah has arrived at his ruling basing on the sound reasoning as follows: It is an acceptable principle of jurisprudence that if a person is prevented from fulfilling any of the conditions upon which the validity of a certain ibadah (act of worship) is dependent, he may still do the same without it, and it would then still be considered as valid. An example is covering the awrah (the parts one must cover) in prayer; while prayer is not considered as valid without it in normal times; but if a person, God forbid, for whatever reasons were to find himself unable to cover himself (either because of having no clothes or for similar reasons), he is allowed to pray as he can, and his prayer is still considered as valid; likewise, facing the qiblah (direction of Ka’bah) in Prayer is an essential condition; if however for reasons beyond one’s control he/she is unable to face it,  they are allowed to face any direction and pray, and their prayer would be deemed as valid. Likewise, if a woman who is menstruating cannot wait in Makkah until such time that her menses stops, then she is allowed to perform tawaf while still menstruating, and her tawaf would be deemed as valid. You could have very well followed this ruling in which case, you would have spared yourself all the aggravation. Anyhow, I pray to Allah to reward you for your good intentions, and reward us all for our best deeds--aameen.