I can't imagine how, unless you know how to do comps. Iff a house has sold near you, that is like yours, you can get that information from the public record. Of course a professional's opinion on whether prices have gone up or down in the meantime would be invaluable. Agents know trends. We know what houses are like others that have sold. For example, I sold a home a year and a half ago for 650,000. 6 mos later the identical home on a comparable street sold for 620000, and recently the same exact home is listed at 599,000 and is going nowhere. Why wouldn't you want a professional's opinion? I would add that most homeowners think their house is better than homes we consider identical, for reasons that have nothing to do with value (I just put in a new driveway, I just got granite ccountertops). Unless you've been following trends for years and can put your ego aside, and look objectively at your own house, you aren't going to come up with the right nunber.
I'd add, forget about zillow. They pick up property transfers and refis, but refis are notoriously high, and transfers don't tell you if a relative bought the house or what the condition is.