Neighbor has denied my access inside my grandma's home. How can he do that?

If your I'D has grandmas address on it this is your residence. Does grandma own the house or rent it? In order for you to be denied access if it is your home an eviction process must be followed that would give you 30 days to vacate.

Something's missing from this picture. Why indeed would a neighbor have any rights at all unless he has some authority of which you're not aware? If not, he has absolutely no right to change the locks or deny you access.

I also don't understand why any locksmith would change locks on a home that isn't owned by the requesting person.

Nor do I understand acquiescing and sleeping in your car. By doing do, you're only enabling the neighbor's alleged authority and dominance over you.

I don't mean to be harsh but my ire is up at how bad this situation has become and the anxiety you must fear, let alone how grandmother would feel if she knew about it.

Get the police involved. Contact APS and find out what the alleged complaints were, and why they now have alleged authority to keep you from the home. If it's determined that your grandmother did not authorize the neighbor to become involved in any way, ask the police to help guide you through getting injunctive relief (a Personal Protective Order) for you, and perhaps your grandmother.

And check the house for theft - who knows what the neighbor might have taken.

Good luck, and don't let this bully run you life!

You said that one day you had a disagreement with the neighbor and had to sleep in your car and it was only after this that you found out the neighbor had the locks changed.

I don't understand.

I don't understand why you slept in your car after having the spat with the neighbor.

Sounds like a landlord more than a neighbor.

Why would you leave your home, rooming w Gma, just because you have a spat with neighbor. Where you in fact told to leave the premises by the owner....aka evicted without paperwork because you were not on the lease. If so without Gma there to let you in I cannot see that you would have any legal standing to access the unit, even if your stuff is there. Must have been one heck of a spat.
A "neighbor" has zero say as to who can enter your home. If you are a legal resident of that home, have ID, can you borrow the keys from Gma? Why do you not have your own set if you live there? If Gma owns the home she determines who lives and enters. If the home is leased it may have restrictions, such as how many people can live there, or whether they require approval hence the landlord may be able to deny access.
Certainly a "neighbor" has no obligation to let you in. Neither does a landlord if you are not on the lease.

If there are unfed animals, call animal control, but do not expect to be able to stay there.

I live in a building w 425 neighbors, people get in spats all the time, nobody leaves their own home over it. They just talk about each other behind their backs. Sounds like there is more to this situation.

Since your grandmother wants you to have a key then have her talk to the neighbor and get the key. Let grandma know what's going on...

so APS cannot deny me entry either right? If my Gma is asked if I can be there she will say "yes".

If you have identification with the houses address on it call a locksmith and tell him you are locked out, then have him change the lock. Or just break in.. But make sure you have an ID..