I have a low resolution image that I know I have the full resolution image stored somewhere on my computer. Is there anyway to search for a JPG on my computer by using a small resolution of an image as an input to search for?
TL;DR: Use Visipics.
What you're looking for is called reverse image search:
[It's a] technique that involves providing a sample image that [the system] will then base its search upon; in terms of information retrieval, the sample image is what formulates a search query.
Those, however, will search among images present on the web; what you need is a tool that will perform reverse image search against the files on your computer.
Well, Visipics does exactly what you need, is free, runs on Windows (2000, 2003, XP, Vista, Seven), and Linux (via Wine). I have used it myself in the past and it is really fast, supports JPG, PNG and RAW, and can have its sensitivity filter customized manually.
From the official site:
VisiPics does more than just look for identical files, it goes beyond checksums to look for similar pictures and (...) applies five image comparison filters in order to measure how close pairs of images on the hard drive are.
Visipic is considerably faster than any other commercial product and (...) will detect two different resolution files of the same picture as a duplicate, or the same picture saved in different formats, or duplicates where only minor cosmetic changes have taken place.