I want to mention that the my camera update code is probably different than what you expect, please take a look over here:

void updateCamera()
{
	if ( D3DXVec3Length( &m_velocity ) > m_maxVelocity )
	{
		m_velocity = *(D3DXVec3Normalize( &m_velocity, &m_velocity )) * m_maxVelocity;
	}

	m_position += m_velocity;
	m_velocity = D3DXVECTOR3( 0.0f, 0.0f, 0.0f );
	m_lookAt = m_position + m_look;
	
	// Calculate the new view matrix
	D3DXVECTOR3 up = D3DXVECTOR3( 0.0f, 1.0f, 0.0f );
	D3DXMatrixLookAtLH( &m_view, &m_position, &m_lookAt, &up );

	// Set the camera axes from the view matrix
	m_right.x = m_view._11;
	m_right.y = m_view._21;
	m_right.z = m_view._31;
	m_up.x = m_view._12;
	m_up.y = m_view._22;
	m_up.z = m_view._32;
	m_look.x = m_view._13;
	m_look.y = m_view._23;
	m_look.z = m_view._33;

	// Calculate yaw and pitch
	float lookLengthOnXZ = sqrtf( m_look.z * m_look.z + m_look.x * m_look.x );
	m_pitch = atan2f( m_look.y, lookLengthOnXZ );
}

The FPS camera is working perfectly, except the little problem that I mentioned (When the up angle is 90 degree and the player try to rotate the mouse up more, right/left start to work which show that the player is rotating around himself).

I have uploaded a video to explain the problem better:

I want to mention that the my camera update code is probably different than what you expect, please take a look over here:

void updateCamera()
{
    if ( D3DXVec3Length( &m_velocity ) > m_maxVelocity )
    {
	    m_velocity = *(D3DXVec3Normalize( &m_velocity, &m_velocity )) * m_maxVelocity;
    }

    m_position += m_velocity;
    m_velocity = D3DXVECTOR3( 0.0f, 0.0f, 0.0f );
    m_lookAt = m_position + m_look;
	
    // Calculate the new view matrix
    D3DXVECTOR3 up = D3DXVECTOR3( 0.0f, 1.0f, 0.0f );
    D3DXMatrixLookAtLH( &m_view, &m_position, &m_lookAt, &up );

    // Set the camera axes from the view matrix
    m_right.x = m_view._11; 
    m_right.y = m_view._21; 
    m_right.z = m_view._31; 
    m_up.x = m_view._12;
    m_up.y = m_view._22;
    m_up.z = m_view._32;
    m_look.x = m_view._13;
    m_look.y = m_view._23;
    m_look.z = m_view._33;

    // Calculate yaw and pitch
    float lookLengthOnXZ = sqrtf( m_look.z * m_look.z + m_look.x * m_look.x );
    m_pitch = atan2f( m_look.y, lookLengthOnXZ );
}

The FPS camera is working perfectly, except the little problem that I mentioned (When the up angle is 90 degree or -90 degree and the player try to rotate the mouse more, right/left start to work which show that the player is rotating around himself).

I have uploaded a video to explain the problem better: