The best way I've found to stop salivating is to keep your tongue gently pressed against the roof of your mouth. You'll only have to swallow once every couple of minutes once you experiment a little bit and get the placement right. As far as your nose running...I've never experienced this, but I HAVE experienced post-nasal drip, which I made a topic about in regards to meditation here:

[URL unfurl="true"]https://www.dmt-nexus.me/forum/default.aspx?g=posts&t=61111[/URL]

Not sure if this is the same thing you're talking about, but it might be beneficial to check it out anyway.