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Looks a little like spider mite ...spray entire plant and be sure to get the underside of the leaves. Get rid of the dead pepper leaves in the pot because bugs use that for hiding spots. You might also prune the old stems back to those new growth stems near the base of the plant. This with encourage more new growth. Your older spindly stems will not be strong enough to hold up new peppers.
Thank you!! This is really helpful!! I just got some spray on Amazon that should be here tomorrow or Wednesday so I’ll be sure to do it ASAP. And I’ll clear out the leaves too. I thought about trimming the stems back but they have some new leaves growing on them already so I wasn’t sure. They’re pretty tiny though so maybe it’d grow even more and be fine? I definitely want it to be as healthy as possible. Thanks again for the help.