Bismillah

Thank you for your question. Although each person should check the rulings of their Marja, the general position of the jurists of the School of Ahl al-Bayt, is that artificial insemination is permissible as long as it does not entail haram touching or looking, and that surrogacy is permissible. There are differences in the details of what is allowed, the main issues being third party sperm donation and the status of the surrogate mother.

May you always be successful