Anything made early on should be accessible without arsenal dwarf, but after a while (either once you get a mayor or after a certain amount of time, I'm not sure) it starts requiring an arsenal dwarf to recognize any newly made items. You can see if something is available for use by trying to assign something as a specific item for them to wear. If it's in the list, it's available. If not, you need the arsenal dwarf to visit his office and recognize it.
I've had no trouble getting dwarves to suit up after having the arsenal dwarf recognize the items being present. You can even specify the exact items you want them to use. I have two of my dwarves using artifact steel battle axes using the specific item assignment. It also works to get them to put on two gloves if they're stupid and are only wearing one - just assign another one specifically and they'll pick it up after you refresh them.
Speaking of refreshing them, I find that sometimes they need a little help to get equipped. After you've set them to wear the stuff and they haven't, go into their orders menu and adjust the uniform option for the month that you are in to "Inactive: Civ Clothes" (M for military, s for schedule, scroll to the rcurrent month and u for the toggle). Once that's done then just make sure they're inactive and let them drop anything they happen to have. Then turn the option off and they'll run and grab the stuff.