Your prayer for peace in your home is heard by God, and your anxious feelings about a new neighbor you have not yet met are completely understandable.
God wants you to live in peace and to know His peace. His thoughts toward you are thoughts of peace, not evil, and He has not forgotten you. The foundation for that peace is first having peace with God, and that is only possible through Jesus Christ. Through the shedding of His blood your sins are forgiven, and the war between you and God is ended. You are no longer living in rebellion against Him but are brought near through faith. Because you are justified by faith, you have peace with God that does not shift when you fail, because it rests on what Christ has done, not on what you do. Grace comes first, and then peace can follow.
From that peace with God comes the peace of God in your heart. Scripture promises that God will keep in perfect peace the one whose mind is stayed on Him, because that person trusts in Him. That is how you can know calm even while living in a world full of turmoil and uncertainty. Jesus said, Peace I leave with you, my peace I give to you, not as the world gives. The peace He gives passes human understanding and will guard your heart and mind in Christ Jesus. The world cannot understand it, but you can experience it as you keep your eyes on Him and trust Him.
You prayed that you would feel His presence and know you are never alone, and that is true. You are in His presence wherever you are. You do not enter His presence only when you gather for prayer and then leave it when you go home. He goes with you, into your apartment, into every anxious moment, and He is with you always. As you walk in fellowship with Him and remain conscious that He is near, His peace can rest upon you.
Let His Word soak your life each day as rain soaks the ground. As you read with an open heart, it will not return empty but will accomplish what God intends, bringing forth joy and leading you forth with peace, strengthening your trust.
It is also good to turn your prayer outward. Ask God not only for quiet but to help you be one who sows peace. Jesus called the peacemakers blessed, and the wisdom that comes from above is peaceable. You can pray for your new neighbor and for the peace of the whole complex, and seek to love your neighbor as yourself by desiring his good as you desire your own. When you sow peace, you reap a harvest of righteousness.
Father, I pray for this dear one who is feeling anxious. Thank You that peace with You has been made through the blood of Jesus. Fill this heart now with Your peace that passes understanding. Keep this mind stayed on You. Make Your presence known in a real way in that apartment, and let there be a quiet assurance that You are there always. Help this neighbor to know Your grace as well, and make this home a place of peace. Give wisdom to be a peacemaker and to walk in Your love each day. In the name of Jesus, Amen.