First, I would start cleaning your teeth daily. Several of the pages on mouth ulcers that came up on Google mentioned dental hygiene. The bacteria that live in our mouths produces nasty, sticky waste that irritates our gums and can cause tooth decay. Anything that irritates your gums can probably irritate the inside of your mouth. Consider gently brushing your tongue, the base of your gums, and the insides of your cheeks.
My current dentist is a fanatic about clean teeth, and when I saw him the first time, he presented some very convincing arguments for being thorough and consistent about getting your teeth clean. I posted his 7 Steps to Great Dental Health
here.
Note: if your gums are already inflamed, they will probably bleed the first few days you use stim-u-dents and floss. Do it anyway. Even if you don't get stim-u-dents and go through all seven steps daily, at least brush and floss.
Other things to consider—vitamin deficiency and physical causes. You mentioned that you've got plenty of iron in your system, but what about vitamin C and B vitamins, especially B12? As for physical causes, is there anything that's causing breaks or abrasions in the skin such as hot foods/drinks, braces, a chipped tooth, rough brushing, or accidentally biting the inside of your mouth? If so, wait for the coffee to cool a bit more, get wax for the braces, see a dentist about the tooth, brush more gently, or whatever.
A couple of articles:
BBC Health Medic8