Okay, I understand why you can't pump. At this point, there is no reason to discourage nursing even if it is "only" for comfort. So much of nursing in a toddler is about comfort, anyway - often more than it is about nutrition. Unless you feel like you don't want her to nurse anymore (which it doesn't sound like is the case at this point), no reason not to let her nurse, however much or little milk she is getting! I think it will probably make both of you feel better. And I think it's really encouraging that she latches 3 times a day. You are STILL a nursing mom!
My kids don't have dairy intolerance, so I'm not the best person to ask about milk alternatives, but I know there are moms who do use other kinds of milk (almond milk, etc) as milk alternatives - if you want some more ideas, you might want to start a separate thread about that specifically. And/or talk to your pediatrician about milk alternatives. In general, though, if you want to encourage solids intake, you could offer solids (including calcium-rich solids) with water to encourage her not to fill up on the milk. The idea is that you want to replace the nutrients in breast milk with other alternatives - in your case it may not be a 1:1, but the breastmilk alternatives may be found in solid OR liquid form, if that makes sense.
It is hard but the hormonal craziness does die down. In my case it took a few weeks, but then I felt back to normal.