hi damo
having been the mother of a 16 year old son in the distant past, but at the risk of sounding like your mother, here are some thoughts:
1/ moms get frustrated about general disorder in their child's room because they unconsciously equate chaotic clutter with not caring about your belongings and not being appreciative of having them, no matter what they are, so if your storage system for your ever-expanding collection resembles cascading piles of boxes and bins, that cover the floor like moguls on a ski slope, start immediately by just keeping them stacked, like with like, or whatever, and give her a path to bring things in to your room and throw things on your bed, or wherever.
2/ i echo the recommendations of the others, shelves, shelves, shelves. if pre-assembled shelving is not an option either because of cost or convenience, an inexpensive and almost instant assembly system is the ages old brick and board shelf system. i see you are in the uk, so i do not know if you have any discount building supply places, but look for concrete bricks (not real ones, they are more expensive) and lumber to stack and make your custom shelves. the bricks can be stacked to customize your shelf height, and the lumber can usually be purchased in various lengths and widths. if your mom fusses about the concrete bricks scratching the walls or floor, wrap them in paper before you use them. store the big boxes under your bed, or stacked together as neatly as possible. if you have limited places to put shelves in your room and your bed is up against a wall, consider pulling your bed away from the wall and put a shelving unit between the bed and wall, you can hide less-used or seasonal boxes below the level of the bed and set up your favorites on the shelves above the bed, although the shelf that is at bed height should probably have boxes and bins on it to keep from knocking things over during the night while you dream about buying more playmobil at an incredible sale somewhere. likewise, tuck another set of shelves between your desk and the wall if possible, or at the foot of your bed.
3/ i do not know if you are a store by set, or type or theme person, but if you have your sets out of their boxes, here in the states there are usually sales on storage containers and bins immediately after the christmas holidays so you might plan your budget to buy some then. set aside a day to sort your collection, you will be amazed at how much fun you will have rediscovering pieces and setting up your favorites on the new shelves.
4/ the best thing about this is it is very portable, so you can use them conceivably forever.
hope some of this helps, good luck.
kaethe