use of verb + んだ and verb + んだけど

Hi,

I'm trying to understand the difference between the two forms "verb + んだ" and "verb + んだけど"

First let's see if I understood correctly the grammar: I have learned that if I want to say that "I have to" to do something I have to use the verb in plain form + のです (in polite form); so for example:

I have to go -> 行くのです

that in informal form is, of course: 行くんだ because の is "shortened" as ん and of course です becomes だ。

If this is right, then what is the meaning when けど is added at the end? I know that けど means "but", even if I found the sentence 行くんだけど translated as "I am going", that actually sould be 行っている.

So probably there's something wrong; could someone please help me to understand better this form? Thanks to who ever will help me.