Vagina is swollen towards the opening and it is irritated a little. Also there is a piece hanging out. Is it normal? (photo)

It appear you have a hymenal remnant.  This is really a superficial procedure which can be performed in the office.  John R Miklos MD

There are three likely scenarios based upon this photo:  a remnant of your hymen, a skin tag, or a wart.  Physical exam will be necessary to evaluate.  This can be easily  removed with a simple office procedure by your gynecologist. 

Thank you for sharing your question.  Though nothing replaces an in-person examination it appears that your extra piece of skin is a hymenal tag.  This is a normal finding but if it has become irritating, it can be removed with a small in-office procedure.  Hope this helps.