is/was wearing

No. Only the first one.

"Just now" means "at this present time" so you need to use the present tense, so "She was wearing the raincoat" is wrong.

Incidentally, this is better, especially if she is wearing the raincoat now, in the present, because the rain occurred in the very recent past:

She is wearing the raincoat just now because it has been raining.

Also, what job are the words "just now" doing in the sentence? They are slangy and conversational and belong to spoken, not written English.

Also, again, unless you have previously been talking about that specific raincoat for some reason, you might say:

She is wearing a raincoat because it has been raining.

Hi Contrex

Just now also means a short time ago, doesn't it?

Yes it does, but it has to be carefully used to avoid ambiguity, since it can also mean "right now".

I was talking to John just now - I was talking to John a short time ago.

I am reading Charles Dickens just now - I am reading books by Charles Dickens at present. It was H.G. Wells last month and it might be J K Rowling (yuk!) next month.

Thanks, Contrex.