well first off lets clear the air that DXM is not an opiate really at all. just derived from them. its usually classified as a dissociative, along with PCP, ketamine, and other less popular drugs.
however, DXM itself is very interesting in how it works. it can be a stimulant, intoxicant, euphoriant, depressant, anesthetic, psychedelic, or sometimes a bit of a deliriant. more info on that can be found
here. read all of section 5 and learn the 4(5) 'plateaus' of DXM intoxication.
however i see something more important in your post. IIRC nyquil does not just contain DXM but also diphenhydramine, the active ingredient in benadryl and tons of OTC sleep aids. this drug is an anticholinergic deliriant and causes a lot of psychoactive effects that are just plain bad. in the future i suggest using something with ONLY DXM as the active drug. my preference is robotussin cough gels since the syrups are absolutely vile to me.
just off what youve said in your OP it sounds like you arent too familiar with DXM and have just heard that cough medication will get you high. i urge you to do your homework. read the link above about the effects and dosage. but also swing by
the dextroverse for a ton of helpful info. make sure to check their warnings page also.
for a direct answer to your question, id say that the paranoia you are receiving is due to your dose being in the range that has stimulant properties to it. another thought is that the paranoia is caused by the strange change in headspace that DXM will cause at any dose.
if you could give me some extra info i may be able to help out more. read the links that ive provided if possible. some helpful info would be: prior drug experience (as in what other drugs, how often) and how much experience do you have with DXM?
sorry for the long read, but i hope it was helpful! =)