I suggest that you seek out a professional speech therapist — preferably one who is a native English speaker. In particular, you should find a professional who specializes in voice. A professional who specializes in voice will be concerned with speech continuity, breath control, pitch, accent reduction, and prosody. Those sound like exactly the things from which you could benefit. By way of contrast, other speech therapists will be concerned with things like stuttering, developmental disorders of language, lisps, and so forth.
In case it isn't clear from what I've said, when you phone the office of the professional you should ask "Can you tell me whether XYZ specializes in voice? Or can they recommend anyone who specializes in voice."
As an alternative, I suggest that you find a singing teacher. It might sound weird but that doesn't matter. Singing is intimately concerned with breath-control, and singing teachers are usually very good at teaching their students how to gain control over their breath so that it lasts through the natural arcs of spoken (sung) language. Do not be put off this idea just because you think you might not have a very good ear for music; you will discover that it is completely irrelevant to solving your problem.
Lastly, if it is impossible to find either a speech therapist where you live, or an English singing teacher, then simply practice singing. If you do this, it would be wise to get a couple of English books that teach singing because they will usually have breath-marks added to the words to indicate where a singer would be expected to breathe.