We understand that you are feeling overwhelmed and exhausted due to the challenging dynamics in your family. The situation with your mother's illness and your brother's lack of cooperation has left you feeling stressed and manipulated. Let's turn to the Word of God for guidance and comfort.
Firstly, it's important to remember that our help comes from the Lord. As it is written in Psalm 121:1-2 WEB, "I will lift up my eyes to the hills. Where does my help come from? My help comes from Yahweh, who made heaven and earth."
In times of difficulty, we are called to bear one another's burdens, as Galatians 6:2 WEB tells us, "Bear one another’s burdens, and so fulfill the law of Christ." However, it is also important to set healthy boundaries and not allow others to manipulate or take advantage of us. Your feelings of frustration are valid, and it's crucial to address them in a godly manner.
Regarding Jesus Christ, we must address this issue of making requests to God. It is only by the name of Jesus that we have access to God (John 14:6 WEB, And Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father, except through me.) Also, there is no other name by which we can be saved. (Acts 4:12 WEB "There is salvation in none other, for neither is there any other name under heaven, that is given among men, by which we must be saved.") If you have not asked Jesus into your life, now is the time. You need to know Jesus Christ to have eternal life and to have a relationship with God. If you need to learn more about this, please talk to a local pastor or Bible believing Christian.
Let's pray together:
Dear Heavenly Father,
We come before You in the name of Jesus, lifting up our sister who is feeling overwhelmed and exhausted. Lord, she is caring for her sick mother and dealing with a brother who is not cooperative. We pray for Your strength and wisdom to guide her through this challenging time.
Father, we ask that You soften her brother's heart and help him see the importance of supporting his family. We pray in Jesus name for a spirit of unity and cooperation to prevail in their home. We rebuke any spirit of manipulation and arrogance, for You do not accept the proud but give grace to the humble (1 Peter 5:5 WEB, "...for 'God resists the proud, but gives grace to the humble.'”).
Lord, we also pray for the medical professionals involved in her mother's care. We ask that You guide them and provide them with the wisdom and compassion needed to care for her mother effectively. We ask your blessing on a change of heart for the doctor to have compassion to be more available.
We also pray for a hedge of protection around the caregiver herself. We ask for a spirit of peace and rest to fill her. We know it is by His stripes we are healed and we know it is by His wounds we are healed (1Peter 2:24 WEB). So we ask these healing stripes to be effective in Jesus name on the caregiver's mother. We know that the effective fervent prayer of the righteous avails much (James 5:16 WEB). So, we pray for a testimony of God's goodness in this situation.
Father, we ask for her Jesus Christ to be Lord of her life and Savior. We ask that she be filled with joy and peace in believing so that she may abound in hope by the power of the Holy Spirit.
In Jesus' name, we pray. Amen.
Remember, the Lord is close to the brokenhearted and saves those who are crushed in spirit (Psalm 34:18 WEB). Stay strong in the Lord and in His might remembering that is His strength and not our own that we live (Zechariah 4:6 WEB).
Prayer Focus: God, Thank You for loving me. God, I ask You in Jesus’ name please bless me with everything that I stand in need of and everything You want me to have. 
