I totally get this!
When my boyfriend 1st suggested a poly relationship, I was more worried about ME dating than I was about him dating other people.
It's fine once you get properly into the 'real relationship' but before then neither parties really act themself. I spend all my time, like you, obsessing over the most ridiculous things and turn quite paranoid, inscure and irrational. Once the relationship has gone longterm, I am the complete opposite but for the 1st month or so - I'm a complete crazy person.
I guess you just have to ride it out. You've definately got the 1st step down (realising why you're feeling what you're feeling), so I guess my advice would be to take the knowledge that a lot of your thoughts/feelings are a little irrational and pick them apart until they become a little bit more objective.
Maybe try coming up with nice ideas for why they're not texting back, they don't even necessarily have to be realistic, just a pleasant fantasy alternative to to the panic whirring around your head. When you take a deep breath and really think about it, it makes a lot more sense.
Also, if the other person is acting a little odd, it could just be because they're getting the new relationship crazies too. Many times I've worried about the whole not-messaging-back thing and it's turned out that they took so long because they were so worried about what they would type and how it would come across to me, etc.
It can also help to let the other person know how you're feeling. Just explain to them that things get a little crazy when you're going through NRE, that you're not always like that but if you seem a bit off, it's probably because of that. They might even be feeling the same (which I find takes a lot of pressure off) and either way they'll be more understanding of what you're going through.