Ouch! I'm sorry this has happened to you. I have a few ideas of what could be the cause, depending on what specifically feels itchy (also, welcome to womanhood... we've probably all dealt with a problem just like or very similar to yours!).
If the skin that you cut/shaved is what is itchy, you might either have gotten razor burn or it's itching because the wound is healing. If it's razor burn, I'm not sure if you know that when you shave you should use some sort of shaving cream, gel, or at least some soap. This helps the blades glide over your skin better. Plus, the skin on this part of your body is much more sensitive than skin on your legs for instance. If you have razor burn, soothing gel like aloe vera can help alleviate the pain, but this should only be done on external skin, not on the inner labia/vaginal area. Razor burn should go away in a couple days so long as the skin stays clean. If it's because the wound is healing, there's nothing you can really do besides keeping the area clean, dry, well ventilated (wear cotton or a similar breathable fabric).
If it is your actual vagina that is itchy (not the labia), this likely means that you have a yeast infection. This comes from bacteria from an unclean surface (maybe the razor, maybe your hands, maybe something else that has come into contact) that has been able to accumulate. A yeast infection also causes extra discharge to come out of your vagina. If you also experience symptoms of more frequent need to urinate (despite not much coming out when you do go) and pain during urination, you might have a UTI (stands for urinary tract infection). Either a yeast infection or a UTI should be discussed with a doctor for treatment before symptoms get worse. If left untreated, sometimes they can go away with proper hydration and diet, but it's best not to gamble and talk to a doctor. Both of these problems are very common for women to experience (some more than others due to biological differences), so don't be at all ashamed to seek medical help.
Ultimately, it is important to always be very clean with everything whenever you're dealing with your genitals and the nearby area. Keep your razor very clean, only shave on clean skin, and put on clean underwear afterwards. I hope that helps!
