Thank you for sharing this so honestly and for wanting Jesus to help you in this struggle. God hears a contrite heart that turns to Him, and your desire to repent is itself a sign of His work in you.
You asked if this is normal as a Christian and if you are not saved because you lost your temper. All Christians still wrestle with sin while we are in this life. Feeling anger is not by itself what condemns you, but God gave us anger not to commit acts of violence against our neighbor or to lash out, but to be vehement against sin and the devil and to correct what is wrong in a loving way. When anger boils over into harsh words or actions against another person, it comes from littleness of mind, not from the purpose God intended, and it can make things worse for everyone. Loud speaking is fuel for that passion, so learning to abstain from anger and to keep our speech gentle is part of walking faithfully.
You are not saved because you never fail, and you are not unsaved because you failed once. Salvation is through Jesus Christ alone, by His mercy and grace, not by our perfect record. At the same time, true faith does not take sin lightly. It leads us to apply the remedies God has given, which are repentance, prayer, humility, a contrite heart, and turning to Him with full assurance of faith. If you have trusted Christ, your hope remains steadfast in Him, and He calls you to draw near with a true heart, confess what happened, and receive His forgiveness and help to change.
That means taking this moment to God without excuse, asking Him to forgive you for acting on anger, and asking Him to help you see where that anger took hold. It helps to turn that zeal inward in a right way, to be a strict judge of your own sin, to scourge your conscience with truth and grace, and to be merciful toward the one you sinned against. It also helps in practical ways to avoid loud speaking and to pause, pray, and step away before responding when you feel anger rising, so that your words remain credible and gentle.
I will pray for you now. Lord Jesus, thank You that You save sinners by Your mercy alone. Forgive my brother or sister for acting on anger and cleanse this wound. Grant a humble and contrite heart, teach them to lift holy hands without wrath, and to use the energy of anger only against sin and the enemy, not against people made in Your image. Fill them with Your Spirit, give them strength to be slow to anger, quick to listen, and to show the same mercy they have received from You. Restore peace where harm was done and help them walk in repentance and love from this day forward. Amen.
If you have not already, go to the person you hurt if it is safe and possible, confess briefly and humbly, ask forgiveness, and continue in prayer and in the Word. God is able to keep you and to grow you in gentleness as you keep turning to Christ.