How to know if you're mentally unstable?!

There are many different categories of mental disorder, and many different facets of human behavior and personality that can become disordered.

Anxiety or fear that interferes with normal functioning may be classified as an anxiety disorder. Commonly recognized categories include specific phobias, generalized anxiety disorder, social anxiety disorder, panic disorder, agoraphobia, obsessive-compulsive disorder and post-traumatic stress disorder.
The definition and classification of mental disorders is a key issue for mental health and for users and providers of mental health services. Most international clinical documents use the term "mental disorder".

There are currently two widely established systems that classify mental disorders—ICD-10 Chapter V: Mental and behavioural disorders, part of the International Classification of Diseases produced by the World Health Organization (WHO), and the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV) produced by the American Psychiatric Association (APA).

Both list categories of disorder and provide standardized criteria for diagnosis. They have deliberately converged their codes in recent revisions so that the manuals are often broadly comparable, although significant differences remain. Other classification schemes may be used in non-western cultures (see, for example, the Chinese Classification of Mental Disorders), and other manuals may be used by those of alternative theoretical persuasions, for example the Psychodynamic Diagnostic Manual. In general, mental disorders are classified separately to neurological disorders, learning disabilities or mental retardation.

Unlike most of the above systems, some approaches to classification do not employ distinct categories of disorder or dichotomous cut-offs intended to separate the abnormal from the normal. There is significant scientific debate about the different kinds of categorization and the relative merits of categorical versus non-categorical (or hybrid) schemes, with the latter including spectrum, continuum or dimensional systems.

wikipedia

Don't listen to some people, especially if these people are not doctors or therapists. Even then, they can be wrong. If they are people who care about you and are trustworthy, I would ask for more Information, but don't take it too much to heart. Find out what they are seeing that makes them want to say this. It is entirely too vague to label you with. What are they really saying? Maybe they are trying to say you are too hot-tempered or cry too easy or something else. Then decide if it true or not and how to deal with it.
People are all a little crazy. We are all filled with both good and bad. We all have our abilities and handicaps.
If these people don't have your best interests at heart, they may be just messing with your head. Ignore them. Focus on someone you admire (a real person, not a movie star) and try to figure out how they do it, what they say, how they deal with each day, etc. Then get on with your life and be the best person you can.
Live well and do good.
P.S. I would never say "You are mentally unstable" to ANYONE.

perhaps your moods are ever changing or possible you are doing or saying things that don't sound right? Are you able to ask these people to explain more why they say this to you.Some people are really sensitive to certain situations and do not cope well with things in life very hard to know sorry not much help so many things it could be.

more details please.