Taylor123 - hi, maybe I can offer some tips for you - please don't hold my active duty Air Force status against me! Whatever was clogging your disposal has now moved out of it and into the main drain pipe your double sinks use. (My mother-in-law had the same problem before.)
First, does your disposal unit have a vent located above the sink? It may have some sort of cap over it that, when pulled off, shows a small pipe coming up, bending back over, and having a small gap between the end of the pipe and the end of the pipe going back down under the sink. If so, check that and make sure it's clear of old food debris. You may need to use a pipe cleaner or Q-Tip to try and dislodge anything stuck/crusted in the pipe.
When that's done, then you may need to go underneath the sink and remove the J pipe. You'll probably see it connecting just below where the two sinks connect into 1 pipe, and the drain pipe leading away from the kitchen area. Be ready for whatever water's in the pipe to spill out when you loosen the connections on the J pipe. Then, once it's off, you'll need to use a plumber's snake to clean out the pipe - force it in a ways, then turn the handle to spin the snake while pulling & pushing it. (You can get them fairly cheap at Home Depot or Lowe's.) The idea is to basically clean the sides of the pipe as you push the snake end down the pipe. If you hit resistance, spin it a few times and then try pushing some more of the snake in...the resistance could be the clog, or it could be a turn in the drain pipe.
Once you're satisfied that you've cleaned the stoppage out, reassemble the J pipe and run some COLD water to check the J pipe connections for leaks. You can then run COLD water for a couple minutes - turn the dispoal unit off and on for 5-10 seconds once or twice while running the water - and see if the water drains away properly.
What I found my mother-in-law doing was (1) putting too much stuff that was too large in size into her disposal unit, and (2) not flushing it through properly. Disposal units aren't normally made to handle the cut-off ends of carrots, bite-sized pieces of steak, etc. - those should go into the garbage can. Also, as I was emphasizing above - use COLD water when using the disposal unit. Hot water can make greases and oils coat the disposal unit lining and they'll eventually catch other food particles, which will start to clog the unit. Cold water, on the other hand, tend to make greases and oils congeal into more solid clumps (like the leftover oils in a pan after they've cooled down). Truthfully, oils and greases shouldn't go down the disposal unit but you can't always drain all of them off from pots and pans...
Finally, always try to run the COLD water for about 15 seconds or so after running the disposal unit. The running water will help carry away the ground-up matter that's now in the drain pipe and get it past many of the places in the pipe where clogs can form.
I hope this is helpful to you. Also, please pass on my thanks to your husband for his service to our country. I hope he's home for the holidays - I'm thankful that I am. In my nearly 30 years of service, I've had my share of time away from home on the holidays and know how it feels. Good luck! Jim D, CMSgt (E-9), USAF/Heathsville, VA (just up the VA coastline from VA Beach...10 miles from where the Potomac River and Chesapeake Bay meet, in the Northern Neck. I also spent 3 years at Langley AFB! Now I'm at Andrews AFB, MD)