How do I continue with filing my taxes if I did not receive a 1099 from my unemployment? Can I get a e-file of this from Mississippi department of employment services?

The state might not have them ready yet.  

Unemployment compensation is taxable on your federal return.  Enter your 1099G for unemployment in Federal>Wages and Income>Unemployment

Go through the screens very carefully to enter any federal/state tax you had withheld from the unemployment

https://ttlc.intuit.com/community/entering-importing/help/where-do-i-report-a-1099-g-for-unemployment-or-paid-family-leave/00/26530

You might need to get your 1099G from the state’s unemployment site when it becomes available in January.  You will need to use the same password etc that you use to certify for weekly benefits

STATES THAT TAX UNEMPLOYMENT BENEFITS

AZ, AR, CO, CT, DE, DC, GA, HI, ID, IL, IN, IA, KS, KY, LA, MA, ME, MD, MI, MN, MS, MO, NB, NM, NY,NC, ND, OH, OK, OR, RI, SC, UT, VT, WV, WI

Unemployment compensation is taxable on your federal return.  Enter your 1099G for unemployment in Federal>Wages and Income>Unemployment.  You might need to get your 1099G from the state’s unemployment site.

STATES THAT DO NOT  TAX UNEMPLOYMENT BENEFITS on the state return

AK, CA, FL, MT, NH, NJ, NV ,PA, SD, TN, TX, VA, WA,