Yes, it is possible to use "ever since" with the present perfect. "Ever since" links two events, a cause event and something that is true from that point in time onward. This is actually ideal for the present perfect tense because one of the uses of the present perfect tense is to indicate that something which began in the past is still relevant in the present. An example of this use is your sentence:
"I always thought it was wrong, but ever since I read it, I've been more confused."
Using the present perfect with "ever since" shows that the speaker has been and is still confused by something which they read in the past.
With the past simple tense, as in your last sentence, it would be more appropriate to use "once" instead of "ever since". This is because "once" links a cause event with something that changed, but does not necessarily link to the present.
Once I did that, it stopped bothering me.
This sentence shows that the speaker was not bothered by "it" as soon as they did "that". It however gives not indication of whether this continues to be true in the present.
I saw your edit, if I understand right you meant to ask if it is possible to use "ever since" and present perfect without past simple, which would look something like:
"ever since" + present perfect + present
Ever since I have been pregnant I feel sick each morning.
The answer is no, this is not natural English. This structure may be encountered in informal English, but it is more natural to have the structure:
"ever since" + past simple + present perfect
Ever since I got pregnant I have felt sick each morning.
I have gone to the US
in the context you are thinking seems weird to me.
But, you are right...
I have been to the US
means you visited the place and came back.
However, have/has gone to not necessarily mean that s/he will not come back. For instance...
Where's John? ~ He has gone to the supermarket. He'll be back in an hour.
has gone... talks about the 'current status'.
To clarify further...
He has been to the US - He visited the place at least once. Visited means went and came back
He has gone to the US - He's in the US. Of course, he can come back!
He was in the US - This talks about his status of being in the US somewhere in the past. We are not emphasizing on the 'visit' (or else it could have been 'have been to the US').
Let me know any other instance that I missed here.
Best Answer
This is because "to go swimming" is a set phrase, meaning to deliberately go somewhere for the specific purpose of swimming. One might swim without "going swimming".
This is coupled with the fact that it is a conventional alternative, when putting to go into the past tense, to flip it to been rather than gone.
Thus, the "haven't been swimming" example may be understood as equivalent to "haven't gone swimming", depending on context. On the other hand, "haven't swum" will mean that you haven't physically swum. That may also be true, but is a different statement with a subtly different meaning, as compared to "haven't gone swimming".
One might also use "haven't been swimming" as the negative of "have been swimming" in sentences like:
That would mean that a person has either been swimming continuously, all the time, for 15 years (which it the sense it might be read as if it were "30 minutes" instead of "15 years"), or that a person has been swimming regularly or habitually for 15 years. The negative might be found as:
Which could mean either a continuous period of swimming, or refer to how long the person has been swimming habitually or regularly.