How do I fix this charging port issue?

You said you had the charging port replaced but something is stuck in the headphones jack. However the charging port and the headphones jack are part of the same replacement flex cable so they are replaced together. Which means if the charging port is new, so must the headphones jack be.

Here's iFixit's guide for replacing the charge port and headphones jack cable if you'd like to take a swing at it. It also contain a link to the replacement part and the needed tools, so you can see how the port and jack are built onto the same flex cable.

Now, let's rewind and start from the beginning:

You need a known good cable to test. New is not necessarily good; it must be "known good" as in verified as working with a different unit both for charging and connecting to iTunes.

You need also to check that your computer USB port is working properly by connecting a different phone as well.

If all the above check out, then you can have: a bad charging port, a bad battery, a logic board failure (Tristar, Tigris, broken trace, shorted line, etc.), or any combination of the above.

(Note that IF the Tristar chip is failing, the iPhone MAY be unable to charge a dead battery, but able to charge a battery that was already holding a charge when it was fitted in the iPhone. Then if you use the iPhone until the battery drains out, you won't be able to charge it again).

You can start replacing parts as per the guide, or take it to a reputable independent repair shop that can perform the proper diagnostic and quote you for the adequate repair. If the failure is at board level, they should be able to offer micro soldering repair.