Why does this happen? You have been speaking English the same way for a long time and associate yourself with your particular speaking style and habits. It is natural for you to feel awkward and maybe even a little embarrassed when you first start pronouncing some sounds differently or making changes in your speaking rate and melody. Practicing in the privacy of your own home is easy because no one else can hear you, but when you feel comfortable with the changes during private practice sessions, it is time to start incorporating them into your everyday speech. This is where you may be hesitant to use them. You might listen to yourself speak and think, "This just doesn't sound like me!"
The bottom line is that it takes about a month before a new habit feels comfortable, and that is with daily practice. No one likes change, and you will naturally resist it when you first start letting people hear the "new you", even though you want to. Your new speaking patterns may feel and sound strange to you initially, so you might think that everyone who listens to you speak may also think it sounds strange.
The good news is that NO ONE will laugh at you or think you sound strange. The changes that you are making in your speech are going to sound much more natural to American English speakers and will help others understand your speech more easily. This is because it will be more in line with what they are used to hearing.
Changing an accent and speaking style are not always easy and, like most things, they take dedication and practice. Don't get discouraged and keep working on it. The results will be well worth it!
You may always have an accent and some language differences when speaking English; getting rid of an accent and differences completely is not the goal. The goal is to create speech that is easy for others to understand, thus eliminating any communication barrier that you may once have had. The key to success in today's society is successful communication, and that is what you will be striving for!