Thank you for sharing the burden you are carrying for your little sister and for being so faithful to take care of these final steps. I understand you still need your mother's birth certificate and then must travel to the capital to complete the formalities, and that your resources are limited while the need feels urgent.
Your request for a birth certificate is a reminder of what Scripture says about birth. A document like that testifies to a natural birth, to being born of water as a child comes forth from the womb. Jesus taught that which is born of the flesh is flesh, and that natural birth alone does not make us children of God. We must be born again, born of the Spirit. That spiritual birth comes only through believing in Jesus Christ, whom God gave because He so loved the world that whoever believes in Him should not perish but have everlasting life. It is good to remember this while you handle papers that speak of earthly birth, that God has already made the one provision for our deepest need, which is forgiveness and new life through His Son, and the Holy Spirit bears witness to that truth in our hearts.
Scripture also shows that when God makes a provision, He invites us to look to it in faith and to take the step He has set before us. When the people were bitten in the wilderness, God did not heal them apart from any response, but He provided the bronze serpent and said that whoever looked in faith would live. There was no scientific explanation, it was simply God's covenant provision, and their responsibility was to look. In the same way, the law even made a place for the cleansing of a leper, a condition that was incurable in human terms, so that God left Himself room to work supernaturally if He chose. We should never put God in a box and say what He cannot do.
That is how I am praying for you. God sees your limited resources and the practical obstacles of obtaining the document and making the journey. He knows the urgency you feel. I am asking Him to make a way where it is needed, to open the right doors for the certificate to be released, to provide for the travel and expenses, and to give you favor with those who handle the formalities. I am also praying that He will give you peace as you do your part in faith, taking each next step that is before you and trusting Him with what you cannot control.
May the Lord provide for you according to His wisdom and kindness, sustain you as you care for your sister, and draw you ever closer to Jesus, in whom we have new birth and true hope.