I definitely break out from those things. I gave up on them entirely because my skin could not handle whatever it was that kept causing them to mess with me.

Anything with soy in it as a major ingredient is pretty damn awful for a person's hormones, and then there's almond milk which can be really hard on the gut... which also, unfortunately, produces acne. Too many nuts will definitely cause you to break out, I made that mistake for a long time before a friend was the one to actually point it out to me. I am not sure about rice and hemp milk because I never tried the protein shake versions of them, but I do occasionally drink oat milk or use it in recipes if I feel like it.

If you want to gain weight, I'd recommend more protein in food, not in shakes. I understand that they are convenient, but people who are acne prone simply can not tolerate them unless you cure your leaky gut/hormonal balance completely in your body and start all over again in a few years. Personally, I wouldn't worry about it and stick to homemade juices if possible, black coffees, lemon waters and just lots of regular water.

Oat milk is the safest milk I drink, if at all. Try making your own protein shakes in a blender at home with that milk instead. I'm sure there are tons of youtubers with recipes. John Venus comes to my mind, but I don't know what he does in terms of protein shakes specifically, but he has a lot of good weight gain advice. It depends on what your looking for. Good luck!