The JD will require certain courses (Civil Procedure, Criminal Law, Torts, Constitutional Law, Contracts, Property, etc.) and allow students to select certain elective course (e.g., Family Law, Immigration Law, Environmental Law). If you are interested in Immigration Law, you would take all the required course and then select electives that focus on Immigration Law. Some law schools may offer special courses of study in immigration law, too -- see UC Davis https://law.ucdavis.edu/academics/certificates/immigration-law-certificate.html and New England Law https://www.nesl.edu/academics-faculty/certificates/immigration-law for example (there are many others - you can research this on-line). And many law schools offer Immigration Law Clinics, where you can practice law as a law student under the direction of admitted attorneys (real clients!) -- see Harvard Law https://hls.harvard.edu/dept/clinical/clinics/harvard-immigration-and-refugee-clinical-program/ and UMass https://www.umassd.edu/law/clinics/immigration-law/ (again, you can research this on-line).
Long story short: the required course for a JD will give you plenty of exposure to other fields of law, and you can use the elective courses and/or clinics to narrow your focus on immigration (or anything else that may have your focus ~7 years down the road!).
Desiree recommends the following next steps:
Here is some other good information I found on collegevine.com: https://blog.collegevine.com/10-best-undergraduate-majors-for-law-school/
I would also look for a non-profit organization that assists immigrants in their immigration cases and work there as much as you can. You will learn the issues and how to deal with them from actually working with them.