I also have high arches and sometimes experience the kinds of aches you describe. I don't know if it's the high arches or not but I tend to be a toe runner. I even used to walk on my toes as a kid until all the teasing from other kids made me stop. The problem with this style of running/walking is that all of the impact of your foot coming down is concentrated on the ball of your foot. Also, your calf muscles contract more. This can make the calf muscles very tight and the balls of your feet very sore.

I'll second Spazzdog's recommendations. Regular stretching has helped me immensely. Also, get a good pair of shoes with proper fit. If you can, go to a running store. They usually have a big selection of shoes and staff who are experienced in fitting all types of feet and running styles. I have also settled on an Adidas shoe as the best fit for my foot type.

I've never visited a podiatrist but I know quite a few runners who have. We have one in this area that specializes in working with athletes/runners. That might help you if all the other suggestions don't work out.