Arko, MdC and anything with Tea Tree oil.
I have had a similar experience with soaps, makes my face irritated. I prefer creams. I have had a comfortable shave with Martin De Candre Fourgere soap.
Soaps that burn my skin:
B&M Cologne Russe
Valobra Fougere & Patchouli (Thankfully Unscented and Czech & Speake doesnt burn)
Speick
Omega Herbae
Fine Lorange Noir & Lavender Pour Hommme
SV Felce Aromatica, Manna Di Sicilia, Tundra Arctica, Stella Alpina, Dolomiti, 70th Anv, & Colonia
Razorock XXX Duro, XXX, XX, X, Stallion, Son of Zeus, Blue Barbershop, Classic, P.160, Tuscan Oud, Don Marco,
Klar Seifen Sport & Classic
Le Pere Lucien Unscented, Traditional & Fougere (Too much coconut oil)
Hendri Et Victoria Unscented (Too much coconut oil)
TFS Il Capitano & Panta Rei
TOBS Jermyn St
T&H Luxury
Lea