I noticed quite a few name brands at the Dollar Store when I was in the US a few summers ago. I don’t know about laundry detergents there, but I thought they had some decent shampoos there. If you find one type too drying, look for a brand that has Ammonium Laureth Sulfate as its cleaning ingredient rather than Sodium Laureth (or the nastier Laurel) Sulfate and some that list some type of oil a little further down in the ingredients list. I know it can be hard because they are listed with their INCI names, but if you educate yourself a bit and learn the name for sunflower oil (helianthus annuus) or almond oil (prunus amygdalus dulcis), you can learn a bit more about what you are buying.
Stay away from those 2 in 1 cheapie products. They may seem to save you money, but they are really bad for your hair.
As a way of saving where I live, I have tried to buy off brand laundry detergent, but our skin is so very sensitive, especially my son and it never seems to clean the clothes as well. I simply buy the larger boxes of the good brands we don’t react to and my per load price drops down to the off-brand price. It is something I use all the time and it doesn’t spoil, so, sure… I have to carry and haul the damn thing home, but it saves me money and hassle in the end.