They don't expire, I've done the same thing: hold onto skill points for several levels (currently, I have 5 unspent points).
If you haven't spent them, it sounds like you might've hit a bug. While there's a chance it might mark you a cheater (disputed), you can use the following console command to get back your skill points:
player.addperk <perk ID>
Where <perk ID>
is replaced with the code for the perk you wanted to spend your points on. The UESP Wiki contains a list of these codes.
But before doing that, I'd double check your perk trees and make sure you didn't accidentally spend them.
Ran some console commands in the name of Science!
First, I leveled light armor to see the effect that skill has on armor rating.
Imperial Armor chest
- 25 armor at 15 skill.
- 33 armor at 100 skill.
Well, that's underwhelming. The rest of the numbers in this post are with 100 light armor skill.
Then I maxed smithing and started crafting.
- 74 - 4 piece leather - no perks
- 119 - upgraded with 100 smithing
- 238 - agile defender 5/5 (cleanly doubled the value)
- 357 - custom fit, matching set (and another 50% on top)
So much for unperk-able leather. How about elven?
- 297 - 5 piece elven armor, agile defender 5/5, custom fit, matching set
- 528 - upgraded with 100 smithing, elven smithing perk
- 610 - upgraded with 130 smithing by using Ring of Smithing (+15) and Necklace of Smithing (+15), elven smithing perk
- 537 - same, but shield-less
Elven armor is the lightest armor I'm aware of. 4 piece is 7 units of weight. 5 piece is 11 units of weight. With this low weight, you can easily skip armor weight reducing perks.
Then I headed off to the enchanting station for one last test. I enchanted with fortify armorer and saw no change to armor rating after the enchant. I recommend skipping the arcane blacksmith perk if you are planning to wear only your own crafted armor. Just upgrade before enchanting. (Ignore what the enchanting table tells you about armor rating, it's wrong.)
That's 2 smithing perks, and 7 light armor perks. With 100 skill in light armor and smithing, you'll be level 26 and easily able to afford these perks.
Can you skip the 2 smithing perks? Possibly. You'll need to compensate by raising smithing skill (much) higher, but if you're already choosing enchanting perks and/or alchemy perks for other reasons...
TLDR:
You can reach 610 armor rating with 9 perks and minor un-perked assistence from alchemy or enchanting. 567 is the armor cap.
Best Answer
unfortunately, the only way the level up is to increase those other skills. Sadly, you can't do the old "go to jail, lose skills, rebuild" from oblivion, because when you go to jail, it removes skill progress, not actual skill.
Fortunately, the game gives you easy ways to lvl up skills:
Complete the Mages Guild quest to get a spell that turns health into magic (equilibrium, i think). Weild equil in left hand (Alteration), heal in right (Restoration) and just cast until mana delpeted [Warning: This CAN kill you]. Make some potions to restore mana and health (Alchemy) before you do this and apply them when needed, and, when casting spells, make sure you're crouching in the middle of town (Sneak) [or in the courtyard of the College, next to the mana pool for faster regen]. Once you've maxed out restoration and alterartion, cast invisible (Illusion) and Fireball (destruction).
Next to combat, equip a Light armor Helmet and Torso, Heavy armor Gloves and Boots and your choice shield. [Enchant if you want] Learn the "Bound Bow" spell (Conjuration)(archery) and go kill enemies in the wild [Ensure to use bound bow during combat to get exp]. Once maxed, go and equip a shield [equip accesories to boost blocking abilities]. Find a companion, take them somewhere remote, attack them till hostile, and then block till maxed (block). [Easy difficulty means you won't take any bad damage]
Finally, Gold Making skills. Craft and enchant 100 iron daggers [look for the best profit enchantment], equip accesories to boost sell prices [or make them]. go to a weapon shop and sell them one at a time to the merchant (speech) [the game counts selling 1000 apple as one apple sold, so you'd get one lot of exp] [Each time the skill increases, exit out and enter again; it will adjust prices]. Once sold, make some clothing that boost pickpocket sucess and (if you have the perk) lockpicking. Then just go around and loot everyone at night, so you have to break into their houses (pickpocket)(lockpicking)
I didn't include one/two handed, because those just require using them.