I know I sound like a broken record but if you are starting solids soon please consider not giving grains. No rice cereal. First foods I would give are sweet potato, avocado and pear. My kids did ok with this so I then gave pumpkin, carrot and apple. First protein was chicken bone broth and then lamb. I then give all fruit and veg. Then egg yolk. Then dairy and all meats. I don't give grain till 12 months. I give plenty of fats and oils in the broths and in coconut oil, olive oil and butter.
It's just really worth looking into things before you start solids so you don't upset bubs already sensitive tummy. Weston a price is a website that might help with first foods.
With the dairy thing..... It can take a good 2-4 weeks for it to completely get out of your body so you might just have to wait a little longer with the dairy free.