I totally feel you, but the more you do it the better it gets. Also, one thing that has made it better for me, is to memorize scripture this should be a daily thing.
Start praying out loud at home with someone or for someone. Pray while washing dishes. I pray around my kids, I use to get a lump in my throat but I refused to give up. I would do it anyway AND it never ever has to be long. it can be very short. I praise while walking down the streets not loud but doing something for 21 days I heard makes it a habit. I pray at church all the time, I am not a good prayer person by no means, but it doesn't matter, Its to God you are speaking to.
I am Adventist and at my church there is prayer all the time. Over everything at the start and end of every meeting and gathering. So believe me you will be called to pray and you can't say no at no time. So what I love is you can pray as long as you want or as short as you want. After talking with my friends at church someone would offer to pray and what a blessing that is.
When praying for someone you should find out what the need is and its really good to know the promises of God. Make it a habit to learn a new promise each week. and pray it back to God. Now if you really want to get God's attention pray back his promises. These are his words that will never come back void. As long as its his will for your life. you always ask if its within your will. Even when praying for someone else.
A week ago I was talking to my cousin/sister on the phone and I was telling her the reason why I have not fallen into despair and she quoted a scripture to me and it blew my mind and lifted my spirits. When you pray for someone nothing will lift them like the word of God and reminding them that God has already made a claim on their life and their situation.
1 Corinthians 2:9
King James Version (KJV)
9 But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him.
this is one of the scriptures I think of when I think of not having a car anymore and having to do things I rather not do. But praying is just a conversation with God and who cares what anyone else thinks. I am still struggling with praying out-loud. I forget folks names or while we are even there. Its terrible, but I press onward, I sigh a lot too. I wish the words flowed easily but they do not. But all that matters is my willingness to communicate with God.