Welcome to HCM.
As he is HIV
positive and tried for penetration and the condom broken it is better to have a screening test for HIV. As it is only three weeks since your risky exposure, it is better for you to go for HIV DNA PCR OR P24 Antigen test. It will come mostly nonreactive. Antibody test will take much time to become conclusive.
may prevent some STDs and not HIV.
Good luck to you.