This is going to depend on budget, scale and how important real-time emissions and pollutant speciation (whether you want concentrations of all of the compounds or specific ones) is to you or your community. There isn't anything quite like the PurpleAir for tVOCs (total volatile organic compounds) or sulfur compounds in terms of cost vs effectiveness, there are some things that come close, some non-real-time options, and some more pricey options for whole communities to scale up if they work together or with existing organizations like air agencies or non-profit groups. Most of what I know is about VOCs, but I'm not sure if the specific sulfur smell you're experiencing will be detected by a VOC or TRS (total reduced sulfur) or H2S (hydrogen sulfide) sensor.
Before you read below, you may want to consider what your goal is for this monitoring data. You may be able to accomplish the same thing by organizing in your community and reporting smells to the local air agency in your area. Most states have malodor regulations which prohibit facilities from emitting beyond their fencelines. If a facility is violating these regulations you can call and report it, and the more people call, the more chance there will be for a response. If you haven't tried this, I'd highly encourage you to do so before trying to monitor it yourself or contact them in conjunction with monitoring and they may be able to assist you. Getting help from professionals and regulators is a good first step as monitoring can be time consuming and costly, and it's good to exhaust all options.
In terms of small scale individual monitors, I'm looking into low-cost real-time VOC monitoring, though there's not too much information about some of the metal oxide sensors currently on the market. I'm hoping to do some collocation testing in the future of the IAQ-Core C, BME680, CCS811, MiCS-VZ-89TE, and SGP30 vs. a photoionization detector (PID). If you have the budget, you may want to check out PID sensors like the Baseline-Mocon eVx, though they can cost upwards of $500 (USD). EPA has an open source sensor based around the Baseline-Mocon PIDs they have been testing around refineries called the S-Pod. I have the documentation for that if you'd like to build it, though it's a relatively expensive project at upwards of $1,500.
Many common community methods you'll see are centered around capturing emissions through grab samples using Tedlar bags or SUMMA canisters (e.g. the Louisiana Bucket Brigade). I think there's some information on Public Lab about the Bucket Brigade and how to do your own grab sampling. This plus lab analysis can be pricey, though some local organizations will lend SUMMA canisters.
I know @ottinger has some expertise in community monitoring, especially around refineries. There are other options that range in price, like open path monitoring using UV-DOAS or FTIR, though for an individual those will be largely outside of your price range. For a community monitoring program with a university, air agency, or other partnership these may be feasible, though come with their own set of advantages and disadvantages. You may be able to do a right to know law request for the refinery in question and get refinery rule data from the refinery's fenceline, though this will only be 2 week benzene data and the averaging times may not be ideal.
In terms of sulfur monitoring, there are some low-cost H2S sensors, which may be what you're smelling, though as far as I know they are largely untested. I believe there was another Public Lab project somewhere on measuring H2S, I think this is it. Someone may have been using badges to measure it, not sure if there's something more real-time-concentration-based.
Here is a list of H2S regulations. I think most of this would be measured professionally using method 16-b but you may have to again submit a right to know request to your local or state air agency to get this information, if it has been measured locally.
Sorry for the length of this response, if you have further questions or need clarification on anything here, let me know.
Thanks again for a super helpful and through posting Karl! I'm just going to ping @sara (whose work you mention in your note) to see if she has any additional ideas about H2S.