Lasse, indeed they can touch you. In fact, they can even kill you.
Alright, I don't have a tulpa and have not ever saw one, but I do know the tales and stories about them, sort of, at least.
Anyway, tulpas can touch you because they are real, but don't have emotions since they don't exist to have one. Let me explain: there are two planed in this world, right? Spiritual and physical? Well, we use to call something Real when we can at least feel it around, like the air, and things that are concepts and completely "unreal", like a dragon, as existent. You see, usually things ir strangle between planes, that both exist AND are real, and things like a dragon, that merely exists, but are not real.
Than you have tulpas. They don't exist, they merely are real. In another way, they miss what is most important, that is the spiritual side of the being, and because of that, tulpas indeed can touch you, but they can't feel it. They do not feel love, they tought love.
Anyway, darling o' mine, I don't think you do have a tulpa, but that's just my opinion. But if you do have one, remember what have I just said.
May the Storm guard your ways.