Hello there,
You definitely have a chance to join Indian navy by the UPSC exam of combined Defense Services (CDS) , there are some posts in CDS, that wants only a bachelor degree in any discipline, so you can apply for them.
Hope I am clear

Hello,
The eligibility criteria for joining navy is
EducationQualification: Candidate must have a qualified in 10+2 examination with Maths & Physics and at least one of the following subjects Chemistry/Biology/Computer science. Age Limit: Candidates should have been born between Feb 01, 1998 to Jan 31, 2002 i.e. from an age of 16 years to 20 years approximately.
You are educationally qualified.
I hope you match the age schemes.
Best of luck