I would prepare your teenagers by letting them know you’re investigating possible causes of whatever symptoms you’re presenting with - I’m sure they’re aware that you’re unwell.
Your GP cannot diagnose MS, only a neuro can do that following all the tests. There are other conditions it may be. Knowing the type of MS will make a difference to the medication you are offered.
Even if it is MS, there’s no need to ‘go to pieces’, you need to be able to answer your children’s questions with facts (as far as possible), not all the horror stories from Dr Google.
Uppermost in my mind at this stage was ‘is it hereditary, will my children get it?’ It’s important to reassure your teens that you won’t have passed it on to them, but their chances of having MS (if it’s confirmed that you do) would have risen a tiny fraction and should they show any symptoms don’t delay in getting it investigated.
As to who else to tell - until you’re diagnosed you don’t have to tell anyone anything. After dx, if you drive you have to tell the DVLA and your car insurance company. If you work it’s up to you if you tell them - and if you do tell HR that it is confidential and you don’t want all and sundry to find out. When you’re ready to let others know that’s up to you.
Take a deep breath and calm down, I can feel the panic in your post. I do understand, I was there exactly two years ago this week. I was admitted to hospital for 6 days so all my family and work colleagues already knew something was amiss, I remember saying over and over “I’m no more ill today (day of dx) that I was yesterday so don’t panic, it’s not helping”. I had to be calm so everyone else was.
Of course I didn’t know anything much about MS at that point
If waiting three months to see the neuro is unbearable look into going private - not as expensive as you’d imagine and if it is confirmed, they can refer you back to NHS for follow up. Chances are you’ll see the same neuro on both occasions.
Take care of yourself and fingers crossed for your dx