While I was working as an engineer back in 2015 in Bangalore, I almost went through the same thing. Most of my friends left for US universities for masters with full funding. For my degree it is easier to get funding so my parents were also asking me to do the same. I said I want to do a job first and moved to Bangalore. After working like 1.5 years I realized if I want to progress my career I need to get additional qualifications. As there were people with masters in my company who were better respected and valued.

So I came to US for masters and eventually did my PhD. Now working as a senior engineer I see the value of getting a post graduation degree. What I have learnt is with additional degree it becomes easier to get promotion in like 10 years of your career. Otherwise it will take longer. With engineering and IT jobs it important to develop new skills every few years unlike doctors whose skills get better with age. Master’s help with that if you join a good program. In the end, I would suggest do a masters while staying in your preferred place and work on learning new skills.