I'd like to shave my head just to see what it's like and then let it grow back, healthy again, it's long normal hair.
I would also strongly advise against it. Of course, it is your decision, and you are free to do whatever you want with your body, but if you are curious about what it's like, one can just watch videos online about people with long hair getting their hair cut short, male or female. Just inspect their facial expressions; I guarantee most of the time, it's not a look of being pleasant. Especially if you watch children, you will see most of them crying. Through almost all human history, long hair was seen as a sign of strength, beauty, vitality, honor, the untameable human spirit. It was a serious offense to cut someone's hair without their consent or even touching it. Most of our gods are also depicted with long hair.
On the contrary, shaving one's hair historically was almost always related to slavery. In many societies, slaves and prisoners were forced to cut their hair short. Many societies had laws that stopped common people from growing long hair, saving it for nobles and kings. Military personnel are also needed to cut their hair short, and, as you know, they don't have free will and work from orders above.
Personally, I think it would be in your best interest to keep your long hair. You said yourself that other people's opinion affects you. In a city of 5k people, it will be definitely seen as 'shocking' to say. If it was a bigger, more 'progressive' city, maybe you wouldn't going to feel as alienated. But again, these are only assumptions and my personal thoughts. I can't know your exact situation.
then let it grow back, healthy again,
I'm guessing that the reason you want to cut your hair is because you don't think it's healthy right now, based on this sentence. This is just my guess, but I can offer a few recommendations. It's easier to hide unhealthy short hair. I would advise you to throw away your shampoo and conditioner. They are designed to make you dependent on them so you keep buying more. I recommend washing your hair with eggs and honey. This way, you'll get biotin, proteins, and many other important nutrients directly in your hair. Use organic, pasture-raised eggs and raw honey. Depending on your hair length, start with one whole egg and one more egg yolk and one tablespoon of honey. Many people think it will smell bad, but my experience tells me otherwise. There is a way around this, though. You can use essential oils, such as peppermint and rosemary, to easily mask the egg smell. While masking the smell of eggs, you will also reap other benefits. These oils are mostly used for their hair-thickening and luscious-hair-promoting benefits. However, you can't use these oils by themselves because they are potent, you need to dilute them with carrier oils. Depending on your hair type, you can choose from many options and combine them. The best combination that I have tried, which nourishes the hair well, is argan oil and coconut oil. Just ask AI to list you the best combinations and choose a combination that suits you best. Mix eggs, honey, carrier oils, and essential oil. Apply the mixture to your soaked hair. Wait ten minutes or more, as much as you want, while massaging your hair and scalp. Then, wash it off with cold water. Do not use warm water. Do this twice a week and you will have great hair.
One last important thing is you need a nutritious, animal-based diet. Your hair only gets the excess nutrition left over after your vital organs and other important bodily functions use what they need. Therefore, a rich diet is very important for hair health.
I hope this helps!