Dynamic port
If I understand your question, then, in short, no.
When your HTTP client (aka browser) opens a connection, the operating system chooses a random port number from a dynamic (or "ephemeral") range.
All messages for this connection continue to use the same port.
Only when a new connection is opened is another port selected.
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To clarify the other end ...
"Standard Application Protocol" servers such as HTTP and FTP have a port assigned to them by the standard IANA body. For example, in the case of HTTP, the default port is "80".
If the client does not choose a non-standard port, web connections are always made to port 80.
The web server always listens on port 80, it never goes anywhere.
Separately, some protocols use "dynamic protocol assignment" where the service protocol number can change, but there is a way to make sure the port number is known.
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