Soap, dry skin, and bar soap?

Hey all...I'll admit my ignorance here at the start, I'm learning, but I have a way to go.

So, I've found that if my skin becomes "dry" then I start to itch, especially when working out, and specifically at the beginning of a workout about 5 minutes in. Its an odd thing, but its very much predictable by time and not very fun. It seems that if I use very moisturizing body washes then I can mitigate most of that problem, but when I switch back to bar soap the problem returns. I'm now trying to add a layer of moisturizer over the bar-soap-cleaned skin to see if that helps.

Anyhow, I have a few observations/questions that I'm hoping the collective can help me with.

1. Through my own testing and observation, I've come to the conclusion that the skin becomes "dry" as a whole, not just in certain sections. In other words, think of the skin like an entire organ by itself. An area that is dry will reduce the total moisture content of the whole organ, not just where the dry spot is. We can mitigate this by moisturizing more than just the dry area. If the skin as a whole is dry, some spots may have symptoms of dryness while others may not. Is this a proper way to think of skin and the generic term of moisturizing?

2. Is bar soap more drying than body wash soap? Specifically I have a bunch of Stirling bar soaps. I love them from a lather and scent perspective, but I wonder if they are a factor in dry skin. I've read that bar soap is not pH balanced to our skin, so the far off pH is a big part of why bar soaps are drying. I've also read that vegetable fats are more moisturizing and should be a component of the soap (as is the case in Stirling). Is this all true?

3. Is a moisturizing body wash intrinsically better than bar soap from a moisturizing/drying perspective? I.e. is the pH more suitable, etc?

4. Is applying a moisturizer after a shower with a bar soap an effective way to mitigate any drying effect from bar soap?

These all seem like pretty dumb questions on the surface, I realize that, but I figured I had better understand the basic principles first before I come up with a solution.

Try phisOderm

1. I've been given the impression that body washes (and most shampoos) are not formulated much differently from dish-washing soap.

I'm sure it (the Palmolive) softens your hands while it strips all the oils out.

2. I strongly suspect that body washes are designed to make you use up the product much faster than a bar soap that does the same thing for less $$$.

3. I like to use Caprina "Fresh Goat's Milk Soap / with Shea Butter" bar soap in the shower. I haven't noticed any drying effects. 
Just for fun, I occasionally use it for shaving lather (I save the end-of-the-bar slivers for this purpose). It collapses quickly, but remains very slick.

I agree John Rose  - I'm a dedicated bar soap guy.  I think the only thing body wash has is convenience if youre showering at the gym or in a work camp or generally away from home but then you still have to have a sponge or whatever to apply it so is it really that convenient over bar soap?

Over the years I have tried a massive amount of both bar soaps and body washes. One of the best body washes with an attention to your skin, is Ethos. It is a higher priced product, but it really was better for my skin than most other products. Prior to Ethos coming to market, my favorites (based on skin issues) were Badedas Original Green Bath Gelee and Algemarin Original Scent Foam Bath – European Sea Algae Aromatherapy...which are both made in Germany, are of extremely high quality, contain moisturizers and are available online at the big A. I have never seen any of these products at a drug store, or big box store. Typically, if you want a specialty product, you will need to seek it out. I discovered those products on trips to Europe.
I have found a very good moisturizing bar soap, that really works. It is from a company which is not well known...Touch of Mink. Their bar soaps contain moisturizers that really work, and are available from the company online. Also, not available in any stores. I discovered this product 37 years ago, and have been using it for many years. I too have sensitive skin and have been fortunate to find products that work.

There are some products designed as shampoos, conditioners, and body washes that can be good for dry skin.

Suave Professionals line has a 3-in-1 product called Shampoo, Conditioner, and Body Wash for Men.
Suave Essentials line has a Body Wash that contains Cocoa Butter and Shea Butter, plus honey and Vitamin E. It should be good for dry skin.

If you have a Trader Joe's near you, one of their best selling products is their No. 3 All for One Shampoo, Conditioner and Body Wash.. It is a great product. It is great for dry skin. It is so slick and rich that I also use it for shaving in the shower when I am in to big a hurry to do a proper traditional wet shave at the sink. If you do not have a Trader Joe's near you, you can order it from Amazon, but expect to pay significantly more than at the store.

A gentler body wash without fragrance may work for you. Cerave and Cetaphil make body washes designated as moisturizing or hydrating. The former also has eczema specific soaps that are good for reducing itch. I'd start there.

As for lotion after washing, go ahead. Some people even slug their face with something like Cerave Healing Ointment or Aquaphor for good effect.

Most likely it is exercise-induced urticaria:

https://health.clevelandclinic.org/runners-itch/amp/

I've had issues with Stirling's bar soaps as well as their Liquid body soaps. They not just dry, but also irritate my skin. I start to get very itchy and end up with mild rashes. I love Stirling, but those particular products don't work for me. PAA and WSP bar soaps work fine, so it seems to be something specific to Stirling's ingredients for me.