Here's what your septic system most likely looks likes:
That outlet leads to a drain field with likely several absorption trenches. Absorption trenches are a couple feet wide and depending on the size of your house, number of bathrooms could be 2, 4, 6 or even more and 20-30 feet long. If you do end up having the guys out to pump your tank make sure you do not have them drive over the drain field. The drain field is likely made up of glorified perforated PVC type pipe. If they crush those pipes with the weight of their truck you're going to need repairs. These repairs are going to cost a hell of a lot more then getting that tank pumped. If the guys that come out are actual septic system professionals they'll know this and will likely be able to look at your yard and know where the drain field is, or have a tool (a thin stainless steel bar) they push in the ground to find the trench piping. The half finished house I bought I could tell where the drain field was by simply looking at the yard. Erma Bombeck was kind of right, the grass is actually greener over the septic drain field.
Right now by the sound of it your system simple can not flow correctly. There just no where for the outlet material to leave the system. This can happen if if you have no standing water above ground. If the water table in the area is even near the surface and rises above the system outlet your system will back up. Speaking of water tables, it's completely possible once the flooding resided the system will begin working on it's own and the tank will not need to be pumped. It's completely possible once the drain field begins to drain the tank level will begin to go down and the system will begin working fine again.
On having your tanked pumped. I've had two houses in the last 20 years. Built one and finished the second (bought it from a guy that got tried of living in a half finished house) they both had septic systems. In 20 year I never pumped my tank once. There several products out there that will help keep your tank flowing smoothly. Rid-x is popular but I'm honestly not that impressed with them. Rid-x claims if your tank needs pumped and you use their product they'll pay for the pumping. I've known two people who tried to take them up on that and both times Rid-x found a reason not to do it. I think one guy didn't keep a written record on how much and when he added the stuff to his tank and the other guy didn't save all his receipts so he had no way of proving he'd been buying and using the stuff. For at least 15 years I added a cup of baker yeast to my system every other month. If you do this make sure you get real bakers yeast, from a bakery. I've been told there's a difference between what you buy on the shelf and what a professional bakery uses. I'm not sure if that's true- but I got my yeast from a bakery and never had to pump. Another key to tank up keep is what you put in it. Limit paper products, you can even buy tank friendly toilet paper. Also don't put fat down your toilet of sink disposable. Veggies and other organic food items down the disposable are fine, but fat and grease will clog the system.
Best of luck, hope life gets back to normal for you soon.