There is no single hormonal contraceptive that works for all women so it takes a bit of trial and error. I would ask your doctor to prescribe a monophasic oral contraceptive (you are currently on something called a triphasic contraceptive). Try it out for a couple months. If you’re still not happy with those few days/month, then skip the placebo week (the last week of the pack) and immediately start the next pack. There’s nothing wrong with doing that and you might enjoy not having a period for awhile.
No it will not impact your future fertility. And no you don’t need to have a period every month to stay healthy.