Here's a better picture of the leaves, hopefully this helps.

A little more info might help.

Is the aphid problem resolved?
What potting medium is it in?
Are you feeding it? If so, what, how much, how often?
What's your watering regime?

answers to Ottawa's questions will help a lot. But my immediate concern is that soil. It looks like plain sand.
Bruce

I second : Answer to Ottawa !

Is the aphid problem resolved?

I believe the aphids are gone, haven't noticed any in the last few weeks.

What potting medium is it in?

Regular dirt from my yard. I live in an apartment, and buying a bag of dirt just for a single plant was impractical. The dirt tends to hold in moisture or turn into a dry rock. It's done both, even in this pot.

Are you feeding it? If so, what, how much, how often?

I give it dirty fish tank water weekly and Osmocote every 3 months

What's your watering regime?

When it looks dry. Had an issue with overwatering several months back, and I went more on the underwatering side of things. Definitely could change this, probably with more dirty fish tank water.

Well it appears the roots are not getting enough oxygen from the extremely poor potting mix. Never use outside soil. The plant is going to die. One way to give the roots some quick oxygen is to put one tablespoon of hydrogen peroxide in one gallon of water. You have to change the soil.

I think you have an solution, transplant the plant into a proper potting medium. You should be able to pick up a small bag at a reasonable price.

Be sure to shake off as much yard soil from the roots when transplant.

Alright I'll see if I can repot it and change out the soil.

I will add though that outside, the soil is reasonably good, despite having a lot of clay and I can usually grow anything I want, aside from cool weather plants. Even in other pot the soil does ok. Maybe it's just past it's use-by date. Either way, will repot

Yah, I thought that soil was looking pretty bad. Regular soil alone is a terrible container soils for peppers. Most other plants as well. you can buy some cheap off brand potting soil that might not be ideal, but will be a lot better than "dirt".

Before you try to transplant that pepper, I would get the soil good and wet first. Otherwise, when that soil crumbles, it will be like cement and will likely trash the root system.

For about $4.00 you can get a bag of Miracle Grow Orchid Mix that is a good soil for peppers and ready out of the bag with some nutrients. You will have plenty left over but it is a good container soil for many plants and you will use it...believe me.
Bruce

Agreed on the soil, it looks like it is planted in concrete. Doesn't matter how good the soil is outside, it gets treated very differently inside and will compact horribly, plus there are no worms, insects, etc to loosen it up.

Alright, so I finally got it repotted in actual potting soil. The roots were spread out all throughout the pot, so it seems at least for awhile it was doing alright. Unfortunately during repotting, most of the small roots were broken off. I feel terrible, but the dirt, even after a through watering, just was not helping. I'm not sure how well it can bounce back from that, but I'm going to try to save it.

I'm assuming the correct course of action would be frequent watering, keeping it warm, and keeping out of strong light for awhile. Is this correct?

Warm is good. I dont know that I would limit the sunlight at all but I would limit the water. Keep it moist, but don't over water. That will only cause you more problems.
Bruce

Give it lots of sun and check the soil by sticking your finger deep in the soil to test if it is still moist. Or you can use a dry Popsicle stick.
Don't water unless it's pretty dry. Also trim it in a place or or 2 and see if new growth pops out after a week. If you get new growth you can do this here and there and you will start developing new heathy leafs.

So I haven't seen much change in my pepper, it didn't even seem to notice that it had been repotted. That being said, there miiight be some new growth. I put it back into it's nice sunny spot after a week.

Unfortunately, I also noticed aphids that seemed to come out of nowhere. There were NO aphids on the plant or the pot before I repotted it, and none of the other plants that I repotted with the same mix have aphids. It's odd, but I broke out the soapy water mix and have been spraying them and the plant when I see them.

I'm also concerned that this potting mix is NOT drying out. It's staying pretty moist, although not dripping wet. I probably should have grabbed a bag of better quality mix, but the alternatives were $8, vs. this for $4. Also, they were Miracle Grow, and I'm decidedly against using MG or most Scotts Company products. (Scotts uses industrial waste in their products)

Anyways, sorry about the spiel, have a picture. Anything of concern that you can see?

For an overwinter plant at this time of year, it looks fine. If your current soil is staying too wet, you may want to remedy that now or face problems in the near future. You could keep the same soil, but mix in some more Perlite or bark. If your plant handled the last transplanting, it will probably be OK with another move right away. The Aphid outbreak is curious. I am not sure if Aphid eggs could survive in the soil or not. I would guess they are from another source and the infestation now is just a coincidence. I have seen where Aphids for some reason will attack one pepper plant and not another. I suppose some are just tastier than others.
Good luck,
Bruce