Welcome to the Forum. It is interesting that your first post talks about an accident and it is good for us to think that you feel we can help.
Re your accidents:
You've been unlucky and maybe a little over confident. OK you are not hurt. Good. You are back in the saddle.
If you are young, your fears should disappear with time - it is merely a question of how much time. You have to tell your subconcious brain, the part of your brain which controls your muscles and instincts, that you are safe on the horse's back.
The brain has got to believe you, otherwise you will tense up and grip and that won't help. You must try relaxing - think positive.
Do some relaxation exercises at homs. Lay on the floor and relax every muscle you can feel - even go to sleep - why not.
Whilst on the horse
Wiggle your toes
Sing to yourself.
Sing to your horse
Take it easy - do simple stuff only.
And use a saddle - you are less likely to come off.
Ride with a companion and talk to them as you go but keep your eyes on the trail and concentrate on what you are doing without tensing up.
Your horse will also now wonder why you are falling off.
He will have picked up on your nervousness
Remember that your confidence helps the horse to feel confident.
Your own tensions will create tension in the horse.
If you have a training arena - or some flat land where you can work your horse
Do some ground work with him/her. Simple stuff - original basic training. - ie barrels, poles on the ground, stops, starts. Voice commands, halts. Stands.
Try getting the horse to do a join up.
When ready do some lunging in circles.
Get back to the stage where you are the boss - but a kindly boss.
Then repeat the exercises under saddle.
Do a half hour at a time, but try to work daily.
Keep the horse interested.
In doing these exercises in a safe confined arena, you are working with your horse and at the same time retuning your own reactions.
Falling off a horse can certainly bring fear but sometimes a fall tunes up the reflexes. It also teaches you a lesson - so watch out for low branches.
It also helps to ride a plodder if available.- a go anywhere, do anything school master - until you get bored with it and then hanker to get back to your own horse.
If there is a trainer local, then it is a good time to ask him/her to look over the way you sit in the saddle and hold the reins. Taking a lesson or two will stop you thinking about how to fall off and start you worrying about doing what the instructor is asking of you.
Maggie. We all fall off sometime. Most of us get back on and within a few weeks boast about how badly we fell off.
Best of luck
PS You were wearing a riding hat - weren't you.