Well done for posting, you are showing courage and strength. You are not just allowing things to overwhelm but you are asking for help and support. You are striving to achieve and overcome this.
You have medication and you are waiting for counselling, both of these are good things.
The medication when you start it will make you feel a little unwell, lack of appetite. You may get an increase to your anxiety, I remember waking up in a panic and taking some time to calm down when I first started, but it was over within about a week. Subsequent increases have not given me side effects. I am curious as to the dose you have been started on, but you don't need to share.
The sooner you start, the sooner you will get the benefits of the medication. It might also be worth speaking to a different GP or the same one if you trust them, and ask about Propanalol, this can be very effective in controlling the symptoms of anxiety.
Consider this, the HV and GP have both seen you, if they were concerned about your children in any way they would tell you that you DH Must be off while you start these tablets and they would refer you to Social Care themselves.
Everything you are experiencing is a symptom of this illness, that does not mean it is not real, but you can notice the feeling and go yet I'm worried, that is because of the anxiety cloud, then decide if it is a real worry or a potential worry. From there you can either act or go yep this is just a symptom, there are no tigers here. This technique just adds a little distance to the thought or feeling.
The brain is amazing but it doesn't always get things right, but it is still trying to protect us and ensure our survival. When it gets used to using the anxiety pathways, it keeps using them and it can take time to teach it, yes that kept me safe when there was a danger but I am safe now and it is a less helpful response.
You are here, you are fighting, you will overcome this. Consider what you would say to a friend in this situation. Mental illness is a real thing, it impacts not just your head and brain but in your heart and gut as well, it can affect you physically as well as your thoughts and feelings. Consider if you had a migraine, or an injury, you wouldn't delay taking the tablets or treatment, doing so can make it worse.
Keep posting, you have more strength than you realise because you are asking for help and still striving.