I'm sure many here will have good advise for you, but if I can just touch on a couple things. One things for sure, when we get a little older...even a teen...a person becomes more self-conscious. Aware of their looks, people watching them, and things that can happen...good or bad...to us. Our imaginations can get away on us.
My suggestions would be to first make sure you ride a very reliable and docile horses which are fairly bomb-proof and easily controlable. But whatever horse you ride...concentrate on connecting with the horse from the ground, talking, grooming, walking (lead and feed), just loving on him and getting to know each other. Let a trust and comfort begin from the ground.
When actually riding, you of course need to start slow and keep in tune with where you are at in strength, balance, and your comfort zones. Let your passion and desire to ride or go faster stay in balance with what you are ready for.
It's like getting used to heights. It is as we get comfortable and confident in our balance and the security of what we are on...that we can go a little higher. And as we are concentrating on the task at hand, our direction, our enjoyment and controls...that we are not so self-conscious. And the connection you develope on the ground with your horse...you take onto the ride. It is a developing of TRUST. Trusting your horse, your ability and your relationship.
And try to keep things simple at first. All kinds of "techniques" and instruction can be confusing and confidence deflating. At any age ENJOYMENT needs to be a priority. It is not like you are out on the range with a boss to answer to in a high pressure job. Be careful who is teaching you too.
Hope this helps a bit.