Is it actually true that anxiety /ptsd will eventually go?

PTSD/ Anxiety: If it is mild it may eventually resolve on it's own. Moderate to severe ptsd may actually worsen over time if not addressed. Some people do have a resolution of ptsd with treatment even if they have significant symptoms. However, for many the aim will be to control symptoms vice eradicating the condition. Simple ptsd is usually easier to get under control than complex ptsd.

Anxiety: Both can be treated effectively with psychotherapy and medication if necessary. Best.