All perfect praise be to Allah
The same thing happened to me brother, and I asked some muftis about this. And they said the solution is to pay compensation of breaking promise with Allah
and start talking with that person, this is only solution. Because it is not allowed for a muslim to not talk with his brother for more than 3 days. In one hadees it says that prayer of this person is not accepted after it. Until they start talking again.
Besides vows of this kind must not be taken in first place, because they are same as vowing to do something wrong.
Sunan of Abu-Dawood Hadith 3268 Narrated by Abdullah ibn Amr ibn
al-'As The Messenger of Allah (saws) said: An oath or a vow about
something over which a human being has no control, or to disobey
Allah, or to break ties of relationship is not binding. If anyone
takes an oath and then considers something else better than it, one
should give it up, and do what is better; for leaving it is its
For details read here.
The compensation of breaking oath is:
“Allaah will not punish you for what is unintentional in your oaths,
but He will punish you for your deliberate oaths; for its expiation (a
deliberate oath) feed ten Masaakeen (poor persons), on a scale of the
average of that with which you feed your own families, or clothe them
or manumit a slave. But whosoever cannot afford (that), then he should
fast for three days. That is the expiation for the oaths when you have
sworn. And protect your oaths (i.e. do not swear much). Thus Allaah
makes clear to you His Ayaat (proofs, evidences, verses, lessons,
signs, revelations, etc.) that you may be grateful”
It is not permissible to move to the option of fasting when one is able to feed or clothe poor persons or free a slave, because Allaah says (interpretation of the meaning): “But whosoever cannot afford (that), then he should fast for three days.” For details read here.
I also broke my oath in the end. And hope you will also do so.
Allah knows best