I have really thick hair and I have been vegan for many years. The times when I lost some hair were when my hypothyroidism was acting up (I have had thyroid disease for 28 years), and when I was severely underweight from an eating disorder. I actually didn't lose my hair then until months into recovering and eating more. There is often a long delay between when something happens that causes hair health to decline and when hair actually starts falling out. So even if you are on the mend, it takes a while for hair to catch up.
What does your diet look like? There tends to be a trend for vegans to eat extremely low fat, and sometimes this can be a problem if you aren't getting enough omega 3 fatty acids. For vegans, this often comes from foods with some fat in them, such as flaxseeds, chia or hemp seed, avocado, nuts (especially walnut), some soy products. Though I tend to eat on the lower end of the fat side, I do incorporate flaxseeds and occasional nuts/seeds almost daily. Not huge amounts, but a serving or two. Some nuts also contain fair amounts of vitamin E, which is good for hair.
I am also a very big advocate of dark leafy greens daily. I even grow my own spinach and collards, and have grown beet leaves and chard too. Leafy greens are big for calcium (at least the low oxalate ones like collards, kale, bok choy) and many trace minerals and iron. Beans are a huge source of iron also, as are pumpkin seeds. Leafy greens are easy to incorporate daily in soups, wraps and sandwiches, salads, smoothies, casseroles, or all by themselves. I also eat several servings of beans each day most days. I think these foods have really helped me.
Eating enough calories is the biggest issue for a lot of new vegans. It is easy to undereat when one first changes the way they eat, especially moving to vegan, because animal products tend to be higher in fat and calorie content in most cases, such as plant versus animal milks, or tofu/tempeh/beans versus chicken or steak. Fruits and vegetables, whole grains, beans, are high fiber and can fill one up long before enough calories are consumed, so it is important to make sure you are eating enough. My weight will drop more quickly if I don't consume at least a little fat in my diet. Weight loss can also mean some hair loss, especially if you lose weight at a fast rate.
Also, chances are if you went vegan you changed your hair products and so on. Maybe what you are using now is making your hair more dry or sensitive? Did you change products? I found that getting rid of alcohol based products and using natural oils really made my hair less dry. Just something to consider.
My Mom tried to go vegan and I witnessed her literally lose half her hair. I wish I would have photographed it as evidence. However, she also eats gluten free, and she can't have nuts or seeds due to severe diverticulitis. So she really restricted what she ate a lot. Gluten free often means eating flours or breads that are stripped of some proteins and natural nutrients that whole wheat flours have (such as iron, B vitamins etc). I tried to get her to at least eat more whole millet, cooked buckwheat groats, brown rice etc. and less processed flour and bread. I had her take a vegan DHA supplement from Deva (derived from sea vegetables) since she couldn't consume whole nuts/seeds. I also had her consume almond butter and sunflower butter, and had her grind her flaxseeds to a fine meal before consuming. But I don't think she was keeping up with this very well (she also tends to eat a lot of junk food and slips off her gluten free diet a bit with bingeing). She went back to eating diary and some fish, and did stop losing hair but I think it was more to do with her eating more calories overall than because it was impossible to meet her needs as a vegan. My Mom doesn't cook much, and doesn' t have the experience with plant based cooking/food prep and open mindedness about food that I do (at the age of 70, my Mom has lived her entire life living and believing a certain way about food and animals), so I think it made veganism more of a challenge for her.
So to wrap it up lol:
eat enough calories and eat a variety of plant food
omega 3/6 fatty acids from nuts/seeds, avocado etc and include some leafy greens daily as well as beans for iron and trace minerals (zinc, magnesium etc)
pay attention to hair products you are using, and keep alcohol based ingredients to a minimum
Make sure your hormones are balanced (have thyroid checked, and vitamin D; are your periods still normal? Are you near menopause? Or closer to puberty?)
I have had screenings and have had my iron/hemoblogin, vitamin D, B12 etc checked every few years, and so far all is very healthy. Most of these tests are inexpensive and easy to do, but vitamin D testing might not be covered by insurance unless there is a medical necessity for it (meaning they won't just randomly check it without a reason...fatigue, bone density loss etc).