I work in Louisiana and live in Mississippi. Shouldn't I get all of La. withheld taxes returned?

No, your resident state will allow a credit as noted below.  Louisiana filing requirements are shown below.

1. Louisiana residents, part-year residents of Louisiana, and nonresidents with income from Louisiana sources who are required to file a federal income tax return must file a Louisiana Individual Income Tax Return.
2. Taxpayers who have overpaid their tax through withholding or declaration of estimated tax must file a return to obtain a refund or credit.
3. Military personnel whose domicile (home of record) is Louisiana and who is required to file a federal income tax return must file a return and report all of their income regardless of where they were stationed.

There is no reciprocal agreement between Louisiana and MIssissippi.  A resident and nonresident return should be filed.  Complete the nonresident state first.

Resident State:  All income worldwide is required to be reported on your resident state return.  Any money that is also taxed in a nonresident state allows you to use "credit for taxes paid to another state" when you complete your resident state return.  Your resident state does not want you to pay tax twice on the same income.  The credit will be the amount of tax charged by the nonresident state or the tax that would have been charged by the resident state, whichever is less.

Nonresident State: Any money earned in a nonresident state is required to be reported on that state tax return (with the exception of reciprocal agreements which does not apply in this case).  The nonresident state will tax any income earned that is derived from that state or while you were in that state for work.