Diploma

Hi,
If you want to study now, that's a good choice. Well, now, you are running your own business. I would suggest you to go for a business Diploma only. Apart from studies, it will also help you to grow your own business in a way. Or, you can do a Diploma in the kind of subject, where you will be taught about the products you are working with in your business. For example:
1 - If your business is apparel based (boutique, design house, apparel store), then you can go for a fashion designing course, or a fashion retail course or apparel designing or can be a textile related course.
2 - If it's a grocery or a general product based bussing, then you should go for a marketing course or consumer behavior studies.
Tell me what kind of business you are working in? maybe, then, I will help you in a better way, that what exactly you should go for.
Good luck!

Screen writing needs language skills as well as creativity. There are lot many language skill courses along with creative writing courses around the world via MOOCs and distance learning. Please choose one.
There are many similar questions that can help you to understand the parallel course required. While doing MA in media management, the career is certainly going towards media management profiles. The managerial profile needs someone with vast understanding of all media profiles and jobs.
I shall still share that there are MOOCs and some distance learning courses to enhance the advertising management and public relations career.
Along with the Master's Degree, an MOOC- Massive Open Online Courses.
Please read the following already available answers:
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-editing-and-proof-reading-course-for-better-career-prospects-qna-4392895
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-m-sc-in-advertising-management-and-public-relations-for-better-career-qna-4392908
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-direction-for-better-career-prospects-qna-4392881
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-documentary-production-for-better-career-prospects-qna-4392890

You can take some MOOCs and short term courses.While doing MA in media management, the career is certainly going towards media management profiles. The managerial profile needs someone with vast understanding of all media profiles and jobs.
I shall not advise equally wide courses as parallel to Post Graduation in advertising. I shall still share that there are MOOCs and some distance learning courses to enhance the advertising management and public relations career.
Parallel courses must be done with care and proper selection.
Along with the Master Degree, some MOOCs- Massive Open Online Courses.
Please read the following answers already available:
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-editing-and-proof-reading-course-for-better-career-prospects-qna-4392895
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-m-sc-in-advertising-management-and-public-relations-for-better-career-qna-4392908
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-direction-for-better-career-prospects-qna-4392881
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-documentary-production-for-better-career-prospects-qna-4392890