Why when I increase my demand for goods and services, they always rise in price? I mean, I know that the demand curve will shift rightward...

Rise and fall in demand is not same as shift in demand
curve. Demand curve is a graph of demand represented on x-axis against market price,
assuming all other factors remaining constant. Thus the demand curve represents the
quantities of goods demanded at various market price provided all other things remaining
constant. The movements along a given demand curve are described as rise or fall in
demand.

The demand for a good is affected by many factors
other than price of the good. For example, demand of a good may change over a period for
reasons like changes in disposable income of consumers, change in life style of people,
change in prices of substitute products, changes in usage of supplementary goods. When
the pattern of demand changes because of such factors other than price the quantity of
goods demanded at every price level changes. In other words, the nature of the demand
curve itself changes. When the quantities of a good demanded at various prices
increases, the curve shifts to to the left, and when the quantities of the good demanded
at various prices increases, the curve shifts to to the
right.

When there is shift of the demand curve to the left
meaning general rise in demand, while the supply curve remains unchanged, the market
equilibrium price, that is, the price at which the demand curve cuts the supply curve,
also shift to the right on the demand curve resulting in higher market equilibrium
price.