I am sorry you had a bad experience. We have all felt frustrated, scared, and ready to give up from time to time. Horses are not easy. With horses, remember a few things....first, preparation is critical. Have you been working regularly in a controlled enviornment (ie arena), with and without a trainer to really get to know your new girl and develop trust and a good seat? If not, I would stay off the trail. It is a common belief that you buy a horse, jump on and ride gleefully down the trails, but unless your horses is rather aged and incredibly well broke, that is just a fantasy. Good, safe trail riding is usually first developed in the arena, IME.
Second, in my observation, a true, trusting, bond between a recreational rider and their horse typically take a couple of *years* to develop, and the more time spent together, the quicker it forms. Five weeks is very early days IMO.
Last, when it comes to trail riding, never underestimate the importance of choosing a good trail partner. Not just the person, but their horse too. You always want to ride with good level-headed riders, but their horse's behavior and experience needs to match you and your horse's needs too. For instance, my very solid trail horse had been out of comission for almost a year due to injury. Now that we are getting back out on the trails, she is very full of energy. Normally, I would not hesitate to go out with a friend riding a green or spooky horse, my horse is typically a calming influence. Right now, however, we need a good steady horse to go out with until my mare gets her trail mind back...and she will. Always choose your partner based on your needs at the time. New horse, new rider, needs very experienced and calm rider *and* horse to go out with.
Hang in there, baby steps, day by day. Never ignore yout gut feelings either. If you feel unsafe, you probably are.