Does touching something cause quantum entanglement? Disclosure: I'm pretty uneducated when it comes to quantum entanglement.
I was aware that there are a few ways for particles to become entangled. Is physical interaction one of them?
I read this question and answer: Quantum entanglement question
Then I thought when I touch something, does that mean that trillion trillions of particles in my fingers have become partially or maximally entangled with the particles in the thing?
Say I touch a wall, is my hand partially quantumly entangled with the wall?
 A: 
Say I touch a wall, is my hand partially quantumly entangled with the wall?

In principle yes, though in practice there is a process called decoherence that removes the entanglement of massive objects so fast that it could never be observed. So your hand is not entangled with the wall in any physically meaningful sense.
The Schrodinger equation for any system (including your hand is):
$$ -\frac{\hbar^2}{2m}\nabla^2\Psi + V\Psi = -i\hbar\frac{d}{dt}\Psi \tag{1}$$
and to understand entanglement the key parameter is the potential term $V$. Suppose we have $n$ particles at positions $r_1$, $r_2$ etc up to $r_n$. If the particles do not interact with other we can write this potential as a sum of a separate potential for each particle:
$$ V = V_1(r_1) + V_2(r_2) + \ldots + V_n(r_n) \tag{2} $$
In this case the Schrodinger equation can be separated into  sum of separate equations for each particle, and the total wavefunction can be written as a product:
$$ \Psi = \psi_1(r_1)\psi_2(r_2) \ldots \psi_n(r_n) \tag{3} $$
This is what we mean by an unentangled system. Each particle is described by a wavefunction that does not depend on the positions of any other particle.
But suppose the particles do interact. Then the potential will contain terms that depend on the relative positions of the particles i.e. it will contain terms that depend on $r_i - r_j$. In that case the potential cannot be written in a form like equation (2), and the wavefunction will not have a form like equation (3). This is an entangled system. It's entangled because the position of one particle affects all the other particles.
This makes it clear what we mean by the term interaction. It is anything that causes the potential to depend on the relative positions of the particles. In the case of physically touching a wall the interaction obviously depends on the relative position of your hand and the wall, so your hand and the wall will (in principle) become entangled.
