The thing about hormonal birth control is that it cause overload of estrogen or hormone fluctuations in the body. When there is too much estrogen in the body (coming from the pill) or too much hormone fluctuations (particularly estrogen) it can cause auto-immunity (the immune system attacks a part of the body). In women this usually result in Hashimoto's, a thyroid disease, where the immune system attacks the thyroid gland.
Do not use hormonal birth control for more than 2 months. Take a break of at least one month after that or else this can cause a permanent damage in hormone regulations.
Coffee (caffeine) is an immune stimulant. Irritability and insomnia after drinking coffee is a symptom of overactive immune system. Either you have a chronic pathogen infection (virus, bacteria, etc) or you have an autoimmune disease.
In case this is Hashimoto's, coffee will cause symptoms of hyperthyroidism (overactive thyroid).
I may be wrong and this can be an allergy to coffee because I don't know much about your situation but the long term use of hormonal birth control and the coffee symptoms seems like you have an overactive immune system.
Does coffee cause hot flashes or make you feel hyperactive?
Did coffee had this effect on you since childhood or is this something that developed as you got older?