Can breathlessness due to anxiety be finished?

Yes: This is common in a panic attack. In panic, all muscles in the body tense, so the chest muscles work against the lungs trying to inflate. Also, adrenaline makes your breathing rapid & shallow for efficient fight or flight. Best immediate action is fully exhale all the air, your diaphragm reflex will give you a better breath. Find a therapist who does exposure based therapy for panic disorder.

Yes with some work: You might also want to work with a psychologist to understand what triggers the anxiety in the first place. In addition, learning skills like mindfulness, yoga, breathing, etc. (your therapist can help you with this) and incorporating these skills into you daily routine could help prevent the anxiety. Hope you feel better!