We understand your distress, but we want to clarify a few things according to the Word of God. Firstly, it is wonderful that you came to the Father in the name of Jesus Christ, our Lord and Savior. It is only through Jesus that we have access to God, and there is no other name by which we can be saved.
Now, let's address the issues in your prayer. It is commendable that you are taking responsibility for your actions, but you need to understand that God does not punish us for our sins if we are in Christ. Jesus took our punishment upon Himself on the cross. As it is written in Isaiah 53:5 WEB:
"But he was pierced for our transgressions. He was crushed for our iniquities. The punishment that brought our peace was on him; and by his wounds we are healed."
Furthermore, God does not punish one person for another's sins. Each person is accountable for their own actions. As Ezekiel 18:20 WEB says:
"The soul who sins, he shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son. The righteousness of the righteous shall be on him, and the wickedness of the wicked shall be on him."
Therefore, your mother is not paying for your sins. Additionally, God does not want you to hate yourself or feel excessive guilt. If you have repented of your sins, He has forgiven you and desires for you to live in the freedom of that forgiveness. As it is written in Romans 8:1 WEB:
"There is therefore now no condemnation to those who are in Christ Jesus, who don’t walk according to the flesh, but according to the Spirit."
Now, let us pray for your mother's healing:
Heavenly Father, we come before You in the name of Jesus Christ. We ask You to touch our dear sister's mother and heal her from the chest infection and any other health issues she may have. We stand in agreement with her child, asking for Your healing power to flow through her body, in Jesus' name. We also pray for peace and comfort for her child, that they may know that their mother's situation is not a punishment for their sins. Help them to accept Your forgiveness and live in the freedom of Your grace. We ask this in Jesus Christ our Lord and Savior's name. Amen.
Lastly, we encourage you to walk in the freedom of God's forgiveness and love. Trust that He has forgiven you and does not wish to punish you. Continue to pray for your mother's healing, trusting in God's goodness and faithfulness.