I am going to try and be delicate and blunt at the same time. I feel sorry that you can't have children, remember YaHWeH is the one that opens and closes the womb. Biblically speaking, if your husband was dead and have no children, then his brother is to go in unto you to give his deceased brother seed.
Deuteronomy 25:5 If brethren dwell together, and one of them die, and have no child, the wife of the dead shall not marry without unto a stranger: her husband's brother shall go in unto her, and take her to him to wife, and perform the duty of an husband's brother unto her.
But since your husband is alive he must ask himself this question, would he be willing to allow another man to squirt his seed into his woman? I pray the answer would be no. Now I know some will say this is different, you are talking about AI, I understand, I get it but you are still allowing another man's seed to be placed into you, no matter how you look at it seed is being put into you, whether by a penis or a syringe. And the one thing that you definitely don't know about the man's seed is was it a homosexual who donated seed? Was it a satanist who donated seed? What is the individual's background and would you want his seed in you? If I am correct, and I believe I am, I have not read in the Scriptures that deals with a man who is sterile. We know the Scripture discusses the woman and how her womb is open or closed, but not a man.
Maybe YaHWeH has other plans for you both and He is testing your Faith in Him. Remember Abraham waited a LONG time for his son with Sarah. We will definitely be praying for you guys.