Don't worry about your veins coming out, that's also very normal. It is probably stress related.
About your point that your perceptions are more accute in this state, that's a fact. I would qualify it more as a transe state than sleep though. The reason we perceive things more clearly in this state is because we're less susceptible to distractions which would decrease our focus.
For your "paranormal experience", you should just take it easy. You seem to stress to much about it. I do believe in the existence of paranormal phenomenon, but most experiences considered paranormal are often easily explained by science.
I get the impression that what bothers you the most is some kind of fear of having something having control over you. That's definately understandable also. Yet you need to do something about it. For example, you could plan potential solutions to the "threat".
Also, if you consider this threat to be paranormal, thus accept it's existence, you could also use the paranormal activity for your protection! For instance you could visualize an absorbing shield around you. It would absorb the bad energies sent to you, and give you strenght to strike the adversary.