No, they are different.

First, you meant to say 降り instead of 振り. (Your computer probably picked 振り込める because it's close to the common word 振り込む which means "to do a domestic wire money transfer").

降り込める sounds strange, but I can think of a couple situations where one could possibly say it. First you need to understand the difference between 込める and 込む. Look up the difference between transitive and intransitive words. Next, there is a grammar where you take a verb stem and add 込む to it to add the meaning of "in" to the verb. Here are some common examples:

• 払い込む "pay in/pay into (a fund something)"
• 送り込む　"send in (troops etc.)
• 教え込む "instill (ideas in the heads of students, lit "teach in")"

So if one were to say 雨が降り込む, the image I have is something like "rain down on (a city/person)". I don't think this particular phrase is common because it sounds too literary (in my opinion).

Now if one were to say 降り込める, the meaning would be similar to 降り込む except this time it's a transitive verb, so in effect it would me "someone (the rain god?) is raining down (something) (on you/someone) and causes the person to stay indoors."

Two final notes about this word. 1) Most of the time, passive form (受身形) is used, so it would become 降り込められる, and 2) instead of 込, the kanji 籠 is also used used (it has the same pronunciation).

So the sentence 一日中、雨に降り込められた means "I was stuck indoors all day because of the rain (lit. I was rained in on all day by the rain)".