If you are not good with soy milk, and it gives you either queezy feelings or you dislike the taste, like others have said, try almond milk or rice milk, there's also oatmilk...
Almond milk is richer in taste, rice milk is still soft, and to me, it has no bad aftertaste or capabilities of giving you a stomach ache, but then, that's my experience. So I think it is good if you see for yourself what you like best.
There's all sorts of alternatives if you are looking for milk substitutes to cook with as well. I never quite understand why someone would use cow milk for cooking though, as it tends to burn. For cooking, depending on the type of food I am making, I use coconot milk, soy cooking cream, almond or rice milk... there's plenty of non dairy milks
Congratulations on becoming vegan, that is wonderful!!