Thank you, that’s really helpful.
Broadly speaking, we have two options:
1. Change to an alternative contraception.
2. Continue with Desogestrel and manage the skin symptoms separately.
A single migraine with aura does convey a very small (but significant) risk of stroke when using the combined pill, so best avoided.
A lower-dose ‘mini-pill’ such as ‘Norgeston’, ‘Noriday’ etc. might suit your skin better. The difference is, that it is important to take these at the same time every day (a 3-hour daily window, as opposed to 12-hours with Desogestrel). Otherwise a coil (either non-hormonal or hormonal) could be used as alternative contraception. If a hormonal coil was used, the progesterone dose is tiny and unlikely to cause skin problems as a result.
As you say, it is quite difficult to see much of the issue on the photo (but thank you for sending, I do appreciate it). I think something quite straightforward such as Adex gel could work if the main issue is some redness/bumpiness. This is a light emollient with an added anti-inflammatory effect due to an extra ingredient, Nicotinamide. It is readily available from the pharmacy without prescription. Like most skin treatments, it will take about a month to have full effect.