I am failing badly at my job!

[Belatedeyebrows]

I gained a promotion this time last year. (For context I work in a school.)
This September has seen more line management and department duties which I was happy to take on.
The team (which was well established) have not taken this well.
I also think I am making mistakes and I can't seem to catch a break on top of my teaching work load.
I'm having to have difficult conversations with staff regarding inconsistencies in the department and I'm rubbing people up the wrong way. I've literally just gone round and "tidied up" things. I've not asked people to do anything that is not already in their job description. I've been mindful not to add to workload and I've tried to consider feelings along the way and facilitate as much as possible.
It's an awful feeling. I know they are talking about me. Some are rude outwardly in meetings.
I always thought I could hold my own but I am sinking and I'm just doing a shit job.
Any top tips?

I think you need to separate the mistakes from the people management issues.

Are you actually making mistakes, or perceiving the team being a bit stormy as a mistake in itself? Which it’s not.

When changes like this happen, it is hard for existing staff to adjust, if they then try to undermine or trip you up it can make things super difficult.

Take the emotion out of this, in your shoes I’d write a list of all the areas you feel you’re making mistakes, and the areas for improvement re the team and ways of working. Try and sort logically

@Cheesetoastiesz thank you.

There definitely was some undermining going on and some sabotage (I hope that doesn't sound too dramatic!)
One is particular, I think I've exposed some of her "busy work" and it's definitely hit a nerve.
Since then, she's been confrontational, rude in meetings (playing with a fiddle toy!) Blowing things out of proportion and not being where she's supposed to be.

I think I've been reacting to her reaction and not managing particularly well in group settings. Confidence and nerves. It doesn't help that she's good friends with 3 of the people who went for the promotion and is very supportive of them.

These types are the worst, and it’s especially difficult to manage this whilst also getting to grips with the role itself.

Do you have an ability to put her onto a performance management plan, you might need to show a display of ‘force’ to get her to either fall in line or to leave, sounds awful but sometimes existing team members just cannot take new leadership. I’ve been on both sides, have had to leave a workplace as I went for a promotion along with a colleague, she got the role and I just couldn’t cope being managed by her, turned into a very different person at work due to it too!

As a teacher l find this kind of petty carry on is quite prevalent in schools and it is really horrible. I have had a few friends retire or change jobs due to a bad reaction to them getting promoted over someone or their friends. Is there any way you could get some mentoring to help you deal with these people as they are only waiting for you to trip up and this will totally destroy your confidence. Getting some mentoring from someone outside the situation is often helpful and will give you space to discuss it all and get some strategies. Always feel those acting like that definitely didn't deserve promotion due to character flaws and remember you were the one deemed fit for the job. Feel certain schools are the worst place for this.

No I'm not able to do that (although if I share my concerns they would be listened to.)
We are in a tight spot of needing staff and she is good at her job hut also likes to be in charge.
I've just had to talk all this through with DH as it's been really getting me down (I can tell him anything but I don't usually bring work stuff home like this!)
I think I've been too kind and I haven't even noticed that she's been manipulative.
I think I can fix it though.
When i break it down I think my management find her confrontational and so have never challenged her. She's been allowed to do what she likes.
I'm now challenging and facing the backlash.
I need to get better at preempting and giving less choice.
Thank you for your advice and experience, I really appreciate it.