This is what I did for 24 years, starting as an EW1 and working up Lead Worker, then trainer and supervisor. I loved it. I do think you have to be cut out for it and it is a lot of work and can be very stressful, at least when I was doing it. (This is probably unusual, but we each did Food Stamps, Medicaid, county medical program and general relief all at the same time. We were not program specific, which was great because we could work all programs. Later I also did cash aid to dependent children, both intake and continuing in all programs.)
We were taking applications, processing all the paperwork, doing budgets, determining eligibility based on the regulations for each program, interviewing clients for initial eligibility, renewing their applications yearly, keeping up with their continuing eligibility based on their reporting changes and on the monthly or quarterly income reports. We had to determine eligibility based on a lot of factors. We first were processing things by hand and it is automated now, but what I found is that you still had to know what you were doing because you want to see the correct results in the system.
I started in 1979 and retired in 2003. I'm sure things have changed, since, so I doubt my experience is much help. I think there was someone on here who was an EW in another county but I don't remember seeing her on this board for a very long time, unless she has changed her user name.
I did feel I could make a difference in people's lives and could make the experience of applying for aid easier for them in terms of helping them to feel more comfortable, explaining thing, etc. Since you asked about whether you feel you can make a difference, I liked it when someone told me I was "just like a real person", and another who told me I gave her hope.