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Dear Shivam,
I can totally understand your dilemma in this case as I have been through the same.
Now, you need understand that there are two important things to consider while seeking admission.
(i) A branch of your choice but from a not so good institute = Not much value.
(ii) A not so demanding engineering branch from a good institute= Not much value either.
As for CSE and ME are concerned, below are some facts.
Computer Science:
Computer Science Engineering is a division of engineering which involves the principles and techniques of both computer science and electronics engineering. It includes testing and designing of computer components.
Some of its specialized fields are: -
Networking
Game Systems
Customer service
Database systems
Embedded systems
Operating systems
Computer Validation
Software engineering etc.
Scope:
The rapid growth of information technology has made computer industry, one of the fastest growing segments. Because of it, there is a huge demand for computer engineering professionals for the development of faster hardware components, new communication systems and software. Computer Engineers with a high percentage of mark and good communication skills can be simply employed in top companies. Software and IT companies are the major employers of these graduates. Some of the top companies such as Microsoft, Google, HCL, Infosys, Wipro, TCS and Mahindra offer a very high salary package.
Mechanical Engineering:
Mechanical engineering has a lot of scope in India and abroad. Some of the areas where these people can utilize their capabilities include the following.
Automobile industry
Aerospace industry
Steel plants
Power generation industries
Communication sector
Railway departments
etc.
Some of the government departments where they can apply are:
ONGC
VSSC
ISRO
IOC
DRDO
SAIL
NTPC
etc.
Some of its specialized fields in Mechanical engineering are: -
Tribology
Nanotechnology
Micro Electro Mechanical Systems
Structural Analysis
Kinematics
Computer-Aided Design and Manufacturing
Production Engineering
etc.
As for institutes are concerned, you can refer to my below comments

Dear Twinkle,
As it will be difficult to provide best institutes, as the definition of best varies from person to person depending on various parameters. However, for the list of institutes, refer to the below link
https://engineering.shiksha.com/be-btech-courses-in-jaipur-ctpg?sort=none&nl=0
(In the above link, you can refine the search as per your city preference)
Before seeking admission in any institute, kindly check the below mentioned parameters such as affiliation, accreditation, fee structure, curriculum, admission procedure, entrance exam patterns, etc.
The basic eligibility for admission in a bachelor’s degree in engineering is successfully completing higher secondary school certificate (10+2) examination with science subject such as physics, maths and chemistry. Admissions are usually done through entrance examinations. However, it is always advisable to get in touch with the institute to get the exact details about the admission procedure as admission process and eligibility vary from institute to institute.
Hope this helps.
Thanks
All the Best.!