I am so impressed with your desire to help your son. Mamas make the best health advocates!
I've had a similar journey for myself and my family, so I hope you don't mind if I share some things I learned along the way.
One overarching principle is that the ingredients that go into making soap, are not what comes out of the soap pot or soap mold. Right now, you are successfully using all those wonderful ingredients on your list -- but without exposing them to the chemical reactions of soapmaking (lye solution + fats/oils). That chemical reaction between lye and fats changes almost everything. It's kind of like baking and cooking: you can use all the best and freshest ingredients, but many of the nutrients in those ingredients are altered or even eliminated by cooking.
In the soapmaking world, the best example of this is coconut oil. For most people, it is very moisturizing in its natural state, i.e., pre-lye. But in a finished soap, coconut oil becomes very drying to the skin, due to its highly cleansing (post-lye) properties. Most sensitive skin folks use fairly low percentages of CO, and some with significant skin issues have to avoid it altogether. Cocoa butter is another soap ingredient that is an irritant to a fair percentage of folks with skin conditions - quite different from how wonderfully moisturizing it is in its natural state.
An earlier post mentioned the two types of soaps that tend to be the most gentle and least irritating to skin: a high olive oil soap, and a high lard soap, both preferably unscented. Those are time-tested and proven. Usually people fall into one camp or the other as to which works best for them. My family has issues with eczema and psoriasis, and we are in the high lard camp over here. It is such a gentle soap with a low cleansing value (that's good - high cleansing = stripping all the natural oils off the skin).
I'd recommend making a small, plain batch of each to start, and see which is better for your son's skin. One bit of good news is that you don't need to add any glycerin. One reason that people tend to prefer handcrafted soap is that unlike commercial soap, the natural glycerin produced in the saponification process is left in the soap. Commercial soapmakers generally remove the glycerin so they can use it for other things, making their soap much harsher.
You can certainly infuse the chamomile into your soaping oils before making soap. Although there isn't any solid evidence that the beneficial properties of chamomile survive the highly alkaline environment + the significant heat generated by the chemical reaction, many people report that they love chamomile soaps. There are some threads here about adding lecithin to soap; most found that there was no change to the feel or performance of the soap.
Finally, and this is a big one: If you want a liquid soap, despite what online blogs and YouTubers may tell you, don't grate and dilute bar soap. The type of lye used to make bar soap (NaOH) will cause your diluted shavings to eventually coalesce into clumpy "snotty" blobs floating in kinda soapy water. No matter how often you reblend it, it will always want to resolidify. So unless you want to grate, dilute, and use up a tiny amount each time you wash him, bar soap is probably not your best option for making a "liquid" soap.
In contrast, the lye used to make liquid soap (KOH) makes a soft paste that dilutes very well in water, and stays diluted. So, if you want liquid soap, make liquid soap! You can even replace much of the lye solution water with glycerin, which helps liquid soap to trace faster, among other things. If you want to make a liquid soap, I'm going to suggest that you read through some of the threads here that talk about how to formulate a very gentle liquid soap.
If you want to make a bar soap, here is a recipe that you could try:
80% lard (find some without additives - usually at the natural food stores)
10% coconut oil
5% cocoa butter
5% castor oil
Beginners usually start with 33% lye concentration and 5% SF. Add 2% honey, based on total weight of the oils in your batch. This will increase the lather, which is normally very tight and lotion-y for this recipe. You could also use 90% NaOH and 10% KOH to increase lather, but that's a bit advanced if you are new to soapmaking. This recipe does best with at least an 8 week cure; 12 weeks is even better if you can stand to wait.
Notice that I left out the jojoba oil, seabuckthorn oil, and essential oils. Those are so expensive to use when you know that the lye is probably going to destroy their beneficial properties. Maybe you can make a lotion out of them for him?
You can use chamomile tea for your lye water, or you can infuse some of your oils with dried chamomile, straining out the herbs before making soap. I would really, really encourage you not to use any essential oils in the soap to start; you need to make sure that his skin can tolerate bar soap first. Make very small batches; 1 lb or 500g is a great size that will give you four bars or so. They do last a long time, especially since you won't be using much on his small body.
Whew, that was a lot! Best of luck to you, and don't hesitate to ask if you have questions!
