Depends on the variety. There are probably 40 or more different varieties of 'chili peppers', some longer, others shorter. So which is it?

As a general guideline, once ripe they don't get bigger.

Dave

Looks just like the Thai Dragons I grew last year. Do they grow pointing up?

Depends on type of pepper, ammount of nutrients available to plant, room for roots (container size can affect this), watering, weed/other plant competition, ammount of light, etc.

What kind is it and what were your growing conditions?

That is how big my Thai chilli peppers grow... I will add though this is my preferred chili to cook with.. In southeast asian countries (I am Indian) we use these a lot... they are small but they pack a good punch.