Yeah, that's a pretty decent jump if they're a 20g or even a tight 18g.
You'd have to stretch your piercings. I would NOT recommend skipping a size. No reason to mess up your ears for cosplay. You can get a blow-out (a gross lip of skin protruding out the back of your fistula) at any size and it would be really crappy to get stuck with that over cosplay.
You could get a pair of 18g studs and see if they fit (since you're not sure if you are at 18g or 20g). If they fit, you'd want to wear them 24/7 for a month and then try a lubricated 16g taper, followed by 16g plugs. And if the earrings you currently have are not a body-safe material you'd want to wear a pair that IS body-safe for a few weeks before switching to them.
If you're at 20g, you'd want to try a lubricated 18g taper followed by a body-safe 18g plug. Wear for a month and then try the 16g.
The problem with smaller jewellery is that it is often too lightweight for the piercing to "self stretch". "Dangly" earrings can do this, but they can also get caught in things at night and tear - like Misseeriechan said, the "cheese cutter" effect of just tearing through your skin.
Neosporin is destructive, pore-clogging and not something you'd want to put on even a wound (there have been studies done about its medical effectiveness and the results are against it - and it's been "praised" as a really great unnecessary allergen for a lot of people. No, like, really - it won an AWARD for that). Sorry, Misseeriechan.
I know people used to recommend it because we didn't have the information we do now (for instance, tattoo artists used it as well but we've come to learn from studies and experience that it actually irritates the site and causes excessive ink loss).
A water-based lubricant is going to be safe - you can even use vegetable oil. If you're stretching properly you shouldn't have an open wound so it's not a huge deal what lubricant you use so long as it's not something that would normally be harmful or irritating.
You could always change the back or convert them to clip-on. If you need to wear them sooner than three months and never wanted to stretch your lobes before this, that would be a WAY better idea.
I really doubt stretching is going to be worth it to you since it's a long process and you might encounter problems along the way and it could take even longer than "normal".
It will also cost you at least $10. So that's something else to consider - can you just replace these cheaper than stretching ? If you can't tolerate the Nickel in cheap "economy" jewellery you're looking at a higher cost, too (and exposure can increase sensitivity - so you could develop a new issue). Acrylic is cheap but it's not body-safe for a new stretch, you want to only wear it a few weeks after you've stretched and still not for extended periods of time.
I'm saying all this because I want you to know what you're getting in to - and that it's probably going to be easier and less expensive to just buy a new pair of modify the ones you have.
At this point, if I was you, I'd worry about changing the jewellery piece, not your body.
You could even just hack off the stud back (if that's what they are) and glue on a new one. Unless they're really heavy they should hold and glue won't come into contact with your skin.