Hi PenelopePaige and welcome!
I can relate to a lot here. I've had an unexplained experience that affected me profoundly, and I've also "studied" with two very pleasant and sincere jw ladies. Since I failed to make satisfactory progress, I'm now "bad association" and very rarely see them.
My take on "supernatural" events is to regard them as "unexplained". Science has taught us a great deal but there are still unanswered questions and always more to learn. And as with Sizemik's example, something can affect us profoundly at an emotional level but have a simple, prosaic explanation.
The jw literature is easy to read and seems to provide authorative answers - at first glance only. Here are a few aspects you might consider when you could be persuaded by any source of information:
Does it persuade or provide a balanced perspective? Is it complete? Are all reasonable objections addressed or only the "easy" ones?
Are sources given for quotes? (and not just Bible quotes). If they are from authorities, are they authorities in that exact field? Are they representing the mainstream viewpoint?
Is it objectively written or is the language loaded? (eg, "honest hearted people will. . .opposers deny. . .)
If the Bible is quoted as an authoritative source, which version is used? is the quote in context and applicable? If the bible itself is "infallible", why does it have internal contradictions?
Most important of all - keep thinking,learning and questioning. The wt will not want you to do that, but if we don't grow, we stagnate. . .
Best wishes and hope you keep posting,