First about your situation with what happened in the UK:
You failed the immigration interview and in such way that they detained you till you could be send home.
I ASSUME you failed on Paragraph 320 7A, false representations, and because of that fail you were served an IS83, which means that they can declare you unsuitable on public policy grounds.
That decision is final and there is nothing (really nothing) you can do about it.
You are not banned yet, but you will not be allowed into the country without an entry clearance (which is often called visa although that is really something else.)
You can apply for an entry clearance but your chances of getting one are zero.
The decision of the immigration officers is final and while they can not issue a ban, the officials that handle the entry clearance can and will if they think your situation warrants it.
Forget getting into the UK for a while.
The part of the law you need to read is P321 (i)
- A person seeking leave to enter the United Kingdom who holds an entry clearance which was duly issued to him and is still current may be refused leave to enter only where the Immigration Officer is satisfied that:
(i) False representations were made or false documents or information were submitted (whether or not material to the application, and whether or not to the holder’s knowledge), or material facts were not disclosed, in relation to the application for entry clearance; or in order to obtain documents from the Secretary of State or a third party required in support of the application.
Link for above:
Now about your question:
Will this situation influence your entry into the USA and other
Yes, of course it affect things.
Your information, including your biometrics have been passed to the other countries working together in the Five Eyes and to the countries working together in the Schengen system.
Those countries tend to take UK removals as a grave event. So of course it will affect you.
And you are now vulnerable to scammers, the organization mentioned in the other answer, the IAS, is just one.
To get out of this situation you will need a solicitor who is experienced in UK as well as USA law, and is a member of the UK Law Society.
You can contact some via this link:
You can contact them by phone or by e-mail, maybe even more options.