If I migrate to America from Jamaica, does that mean I can go anywhere in America?
If you legally emigrate from Jamaica to the USA, then as a visa holder, there will be restrictions on how long you can LEAVE the USA on trips abroad (only short trips are allowed). You may travel within the states just as any other legal resident can. With one possible caveat. I think you have to have certain documentation on you at all times for anything other than casual trips. I know you have to have this documentation if you leave the country in order to get back in, and I think you're supposed to keep it on you. It's nothing complicated - just your passport and proof of residency card (or whatever that card is called now that has your permanent address in the US on it). If you become a citizen, of course, this is not required and you can freely travel between the states even without an ID - if you walk or ride with someone else - because an ID is required to use trains or airplanes, or to drive a car, you must have a driver's license.
Caveat: The two states you cannot visit without some form of ID are Alaska and Hawaii. If you drive to Alaska, you have to go through Canada. If you take a boat or fly to either one, you have to leave US territorial waters or airspace. Thus, you will need an ID.
US citizens can go to any public place in the United States that is not subject to restrictions. There are for instance some public lands set aside as wildlife sanctuaries that you may not enter, and military bases are owned by the government but are not open to the general public. There are no borders between the states except for some agricultural inspection stations such as those between California and Arizona.
Do you mean Migrate = to travel, or immigrate = to becoming a citizen?
As a traveler/tourist you are able to go from State to State freely but you cannot stay anywhere forever. You have to Immigrate to do that.
Exclusive of some government owned property, the Fort Knox Gold depository, Area 51, Military bases, etc. you can travel to any State you want.