Should I open up my own personal trainer studio?

This would depend upon a number of factors including; your financial backing, location, your business experience in terms of marketing, selling, financial planning and having a service which offers in my opinion more than just blocks of 5 or 10 personal training sessions as your main selling point.

Opening up your own personal training studio is certainly a serious consideration when you have the necessary experience and business skills and ongoing mentoring. If you believe you have the necessary skills and backing you should certainly consider it.