Convergys is a customer experience outsourcing group that has a global presence. Since you have a sound experience on customer service, why not build on it.
The core skills desirable in any customer service sector would be good communication skills,leadership qualities,ability to effectively use computers, feed back etc.
The other issue to consider is in Convergys which sub-section were you under - healthcare, travel, finance etc. This would also enable you to build a career oriented education.
Here, you can consider, Human resource management, marketing, accounting, corporate net security etc.
You can look into the options of
Bachelor of Science(Hospitality and Hotel Administration).
Diploma in BPO Finance and Accounting
BCom with Major in Corporate Affairs and Administration (BCom (CA&A))
BCom with Major in Financial and Cost Accounting (BCom(F&CA))
you can plan your MBA.
All the above are available at IGNOU.
All this would take time. Choose a course that should help you with your desire to move abroad, if not, it should help you to enhance your present job promotion chances.
Can you discuss with your employee counterparts places overseas and plan. Please also check for careers overseas listed in your firm itself and try your luck