Nita, I agree that the first thing you need to do is to get her to the doctor. You don't have to tell Mom that you are going to have her assessed for dementia. Just take her for a physical. Be sure to tell the doctor what is going on with her and ask him to do a MMSE (Mini Mental Status Exam). This will give a quick view of her cognitive status. There are 30 questions with 30 being a perfect score indicating no problem. The lower the score the worse the problem. Then her physician can make the necessary referrals. Yes, it is a scary diagnosis but knowing what you are dealing with will help you tremendously to make the necessary plans for the future.
Know it is typical for those with dementia not to realize they have a problem. Because of the damage to their brain, they believe they are functioning well. It is NOT normal aging or forgetfulness. If something "slips our mind" we can retrace our steps or find a way to access that memory. We know that we have forgotten. For them, it never happened, it never existed. So they have no clue what they don't know. There are holes and gaps in their recent memory that just do not exist. Their mind will fill in the blanks so it makes sense to them. Their reality is as real to them as yours is to you. If they can not accomplish a task they make an excuse or ignore the problem. At times they seem almost normal and at other times they can not function. It not only affects their memory. It also affects their ability to make decisions, their ability to reason, their behavior, their ability to follow directions, and so much more. Some of the things to look for is inability to keep a check register, pay bills, or keep track of money. New technology such as computers, TV remotes, and telephones become difficult for them to use. They may put something away and then accuse you of stealing it. They may put a pot on the stove and then forget it is there. They may not take their medications or may take too many. They may wear the same clothes repeatedly, refuse to take a bath, or change clothes repeatedly. As you have seen they may forget important information. They can also get lost in familiar surroundings. If she is driving you definitely need to have her assessed for her cognitive ability to drive. To know what to do in an emergency situation.
Yes, it is overwhelming, especially at first. You are busy with your life and this takes time to sort out. Typically it is one siblings that ends up with the brunt of the burden. Yet it is something that is done and that you can do. It just takes time to get your bearing, bet your diagnosis, and get a plan in place.
I would advise that you get outside help for your Dad to help him with Mom. Introduce them as a new friend. Let the care giver come with you a few times until Mom gets used to having her around the house. Then she can come in to "visit" when Dad need to go out or just needs a break. As the disease progression you will want to add additional help as needed. At some point it may be necessary to place her in a facility so you need to investigate what is available in your area and how to pay for it. It is always better to be prepared than to be scampering at the last minute.
No, you are not alone, and Yes, you have found the right place

All of us here are dealing with the same. My Dad was diagnosed with Vascular Dementia in 1998 and passed away in 2010. Mom was diagnosed with Alzheimer's in 2006. She is now in a specialized locked dementia unit in the final stages. Back in 98... it was rather overwhelming. Today... it is my normal

It is not what we want to do but what we need to do and what we do!! Welcome, and hope to hear from you often...
Love, deb