Welcome to SRP!

Mt first thought is that your problems started when switching shaving soaps, so you may be allergic to the new products. Give it another go or two and if the irritation persists set them aside or sell them. I usually recommend using alum immediately post shave, and you could try it but I still think it's a skin reaction to the product.

Second thought, cut out the ATG shaving for now, especially when you start DE shaving. That is a major source of irritation, and usually an XTG pass will get the job done.

Third, you may want to nail down the source of irritation with your cartridge shaves before moving on to your new DE. DE's shave wonderfully, but they do take an adjustment of technique and there is a learning curve. You'll have to learn what no pressure means, and as I mentioned, you may want to lay off the ATG pass for awhile. Don't worry too much, it's fairly easy. The 38C is a great razor, it's heavy so you let the weight of the head do all the work for you. I'd recommend starting with the Astras, which are better for a beginner than the sharper, less forgiving brands you got in the blade sampler.

Good luck.