Tedvio, the Australian poster nailed the bac water and alcohol piece, that's the part most people get wrong. Bacteriostatic water inhibits new growth but doesn't kill what's already in the vial. Same problem with the alcohol swirl approach you described. Alcohol needs full coverage and adequate contact time to actually sterilize and you can't guarantee either by swirling it through a sealed vial.
The cleanest approach if you're filtering for sterility is to use vials that are sold pre-sterilized from the manufacturer with documented sterilization method. Steam autoclaved, gamma irradiated, or dry heat at 170C for 60 minutes. That info should be on the listing. If it's not listed, treat the vial as not sterile.
Pen cartridges from reputable suppliers come sealed sterile and the packaging usually has a sterility indicator. That's a solid option if you don't want to deal with stoppers and crimpers.
If you're committed to sterilizing your own, a pressure cooker can work but you need to control temperature and time properly. Dry heat in an oven at 170C for 60 minutes also works for glass vials but the stoppers can't go in the oven, those need either irradiation or steam autoclave.
One thing to keep in mind, the .22 micron filter is what actually sterilizes your solution. The vial just needs to be sterile when it receives the filtered liquid. So the sterility question is really about the vial and stopper, not the peptide itself.