brief pain and swelling in hips during intense movement
I'm with Batman in that you should contact a medical professional. This sounds way too serious to trust to what some random people on the internet say. However, if cost is an issue there I can make some suggestions about some things you can do to prevent some common bike-related injuries in the future (after you see a professional or did something else to get rid of it). 


Did I already say you should really see a professional? This isn't normal at all, and really sounds like something you should have checked.
Get your bike set-up properly. Go to a local bike shop to some help, or google around for something like this. Note that it is very much possible that your bike is too small or too large for you, in which case there is nothing to do but get a bike better suited to your size.
Fast or heavy pedaling? You should use your gears! Optimal pedaling frequency is around 80-100 rotations/min. Lower than 60 puts a serious strain on your joints. If you can actually produce useful force above 140 I applaud you but that speed is also inefficient and strenuous. Try to change gears more often, if you need to go lower or higher than you can regularly then get lighter and/or heavier gears.
Did you recently increase the amount of cycling you do? Though mostly a low-impact sport cycling can still cause injuries, and you should increase your workload slowly over several weeks or months depending on your age.
Seriously, go see a professional.