So when I was younger I made a promise with God concerning me taking trips on planes (I’ve never been on one due to this experience).
Do you believe that God asked you to make this promise to never travel on a plane, or did you have a bad experience and then say "God, if you get me through this, I promise that I won't travel on a plane again"?
One is from the Lord, asking you not to do something or saying it is not his plan for your life; the other is you bargaining, or making up your mind that this is what God wants for your life - big difference.
I was unable to fulfill this promise and I even went as far as to say “give me one final chance” (in prayer of course) that however didn’t work.
How didn't "it work"?
Anyway I’m a firm believer in temporal punishment and believe if I do get on a plane I’ll probably die.
Jesus died for your sins. If God was going to punish us every time we sinned, there'd be no need for Jesus to have come and suffered the cross.
I’d love to travel one day but just thoroughly reading through the Bible, I don’t think even repentance could help me.
Sorry, but I don't think you can have read the Bible that thoroughly.
All through the OT God told the nation of Israel that they would be punished unless they turned from their sins and turned back to him.
Ahab was a wicked king, but God spared him when he repented.
Peter denied Jesus and was given another chance - he wasn't even perfect after that.
Jesus taught us to forgive 70x7; he would not ask us to do something that even God was unable to do.
Jesus taught us to pray, "forgive us our trespasses".
John said that if we sin we have someone who speaks to the Father in our defence, 1 John 2:1-2. And that if we confess our sins he is faithful and will forgive us, 1 John 1:9.
There has been countless of biblical examples of God ignoring people’s prayers
God answers prayers; it's just that the answer might not be what we were hoping for.
I don’t feel any different. The promise went on saying “God please don’t kill me on a plane if....” or “please kill me on a plane if I....”.
Like I said, was the "promise" something which the Lord asked you to make, or something that you just decided would be a good idea?
Why not ask God? Why not say, "look, I'm sorry I made this promise; it was me trying to bargain with you and was wrong. If you clearly tell/show me that you never want me/it would be a sin for me to get on a plane again; I won't. Otherwise, I repent of this promise that I made, and pray that you release me from it"?
Then listen to him; be guided by God, his word and his Spirit. He hasn't killed you yet, so what's making you believe that he will?