Should I do an MA in TESOL and CELTA?

Hi! I'm an Indian teacher with less than a year of experience teaching English as a Second Language. I have a CELTA from the British Council in India and I've been thinking about applying for an MA in TESOL to improve my theoretical foundation and (hopefully) improve my job eligibility. Since I did my CELTA in India, I have faced some hurdles when I applied for jobs in other countries, primarily the label of "non-native English speaker".

Would it be helpful if I did an MA in TESOL from the UK/US/New Zealand/Australia/Canada/South Africa? And how useful is it to have both qualifications? Does it make sense to do both?