The following comments are based in my decades of experience surveying on both coasts.
This example is one of the reasons that I would not live under an HOA and I live outside the city limits.
You have two issues here.
The first issue is the HOA. They get there authority from typically either a deed restriction of Covenants, Conditions and Restrictions, commonly called CC&R's, either of which should be listed in your title insurance policy as a schedule B exception. If you were not provided a copy if the document the title company should send you a copy if you request it.
You also need to go through all of the paperwork that you have related to the purchase of the property looking to se if there is an existing survey. They survey requirement varies by state, some stares require a survey and some do not. also some states require the survey to be recorded.
Also check the square footage if the property to make sue it is the same on the listing, appraisal, tax bill and contained in the deed.
The second issue is the real property. This issue has two main parts. The first part is what land was actually deeded to you and the second issue is prescriptive rights.
First you need to have a local surveyor review the documents, including your title insurance policy and the warranty deed your neighbor has, to determine what property is contained in the deeds and what easement and other rights you have.
The second thing you need to do is talk to the surveyor, or a lawyer, about a claim of prescriptive rights to the property. The laws for prescriptive rights vary by state. In some states occupation is all that is required but in other states it is next to impossible unless you meet some very specific requirements.
I would not move anything until you receive some professional advice. Moving could adversely affect tour potential claim of prescriptive rights. If your neighbor notified you in writing then the clock is probably ticking, but you would need to consult a lawyer to know for certain.
In the end you will need to consult a surveyor, possibly a lawyer and potentially file a claim with you title insurance company.
Be prepared to spend some money to sort this out.
Good Luck