I work as a project coordinator, am I eligible for the PMP course and exam?

100% you are provided you have 3 years of work experience after your Bachelors Degree. PMP is a globally recognized certification from PMI-USA.

Absolutly by all means below are the eligibility criterias :
To apply for the Project Management Professional (PMP)®credential, you need to either:

Possess a Secondary Degree (High School Diploma, Associate's Degree, or Global equivalent) with minimum of five (5) years / 60 months of unique (non-overlapping) Project Management experience, with 7,500 hours in leading and directing projects, and 35 hours of Project Management Education

OR

Possess a four (4) year degree (Bachelor's Degree or the Global equivalent) and a minimum 3 years/36 months of Project Management experience, with 4,500 hours in leading and directing projects, and 35 hours of Project Management Education.