Hello!
I've been diasgnosed with schizoid personality disorder and my opinion is, of course you can improve! Schizoid personality disorder is less serious than actual Schizophrenia, for example. Also, from my experiences, I have improved so much.
I was very shy as a child, started seeing psychologists at age 3. I wasn't playing with other kids, didn't talk much ect... It stayed like this until age 17 with some small improvements, but so small that it wasn't visible. At 17-18 year old, I was lacking social skills and I didn't care much about social life and friends. I also didn't care about my personal hygiene and my looks (I never bought earrings, beautiful clothes to emphasize my looks...)
Then, at age 19, I started going to psychiatric center with nurses and all (not mental hospital), where people had activities there (cooking, drawing, exercising, theater etc...) So I started to be around people more as I was in that center. And slowly, my shy traits started to reduce, I slowly began to feel interest in social life and began to care about my looks (I started putting some makeup).
My introvert personality slowly turned into extrovert one. It was slow and progressive, but it was there.
Until age 25 (now), where my improvement has reached the TOP!!! Nowadays, I'm totally a different person than before! I don't only feel more interest in social life, but I LOVE being around people! It became a NEED! I can't stand loneliness anymore. I hate being alone. I love people and meet new friends! I often see myself being hyper-talkative now! My shyness is totally GONE. As for my hygiene and looks, I now really love to take care of it! If you enter my bathroom, you'll see it looks like a skincare & beauty products STORE! Lol. My bathroom is full of these. I also have a wide collection of earrings and jewelry. I love to take care of myself now. When I look at my former self, I usually have this thought : HOW COULD I BE LIKE THAT? Social life is so fun, self-neglection is bad, taking care of myself is so much better! I enjoy all these things now!
I won't say my schizoid traits are cured, because unlike depression, it can't be cured. But I have improved SO MUCH!
So please, don't lose hope! You can improve!