Just a possibility, but the timing belt drives the water pump on the
4-cylinder engine in the '96 Camry. (Don't know about the 6-cylinder) My wife's '96 had a coolant leak that I had not tracked down yet when the timing belt broke, thereby stopping the car dead in its tracks and alerting us to the fact that the water pump was the source of the leak. (I worked in a radiator shop for 25 years--you would think I would have figured it out before then---I hadn't been able to find the water pump by visual inspection--it is behind the timing belt cover--and was begining to suspect it as the culprit, but just put off checking it out a little too long. I guess after a quarter century of working on car cooling systems, I just don't even want to think about them any more....I prefer working on computers now...which is not much different from working on car cooling systems, in some respects, nowdays....) In any event, we needed a new water pump, and a new wp housing due to the fact that the bearing had worn to the point that the impeller had worn on the inside of the housing enough to make it a good judgement call to replace it, timing belt (antifreeze had soaked it and caused it to fail) and it was time for the 120,000 mile check-up, so it was a good bit of money later before we drove into the sunset. I don't regret it though, it's a very good car and it's worth keeping in good shape and dependable so that it doesn't strand my wife somewhere. I suggest that you check out the timing belt and see if it has parted. You can take a couple of bolts out of the cover and see. You may have to turn over the engine and see if the cam gear turns--if it does, the belt is intact, if it doesn't, it's not. The 4-cylinder is a non-interference engine (the valves don't stick far enough down when fully open to hit the pistons at any time--yes, many people make engines that DO have the valves hanging there to be hit--Honda and Nissan do it frequently, IIRC--so you have very little chance of damaging the top end of your engine, but I'm not there, so I can't say for sure--YMMV), I don't know about the 6-cylinder.
Overall, if you are not a mechanic, I would humbly suggest you ask around and find a mechanic who is recommended by people you know as being a good, knowledgeable, HONEST, mechanic. Notice that I did not include low rates as a criteria. In 25 years of working in the automotive business, the one consistent thing I found was that the people who got screwed the most were the ones who insisted on paying either the least or the most. The ones who tried to scrape by on the cheapest parts/labor might get by for a while (sometimes a pretty good while), but almost without exception in the long run they wound up paying more. It just catches up with you. The ones who sought out the most expensive people to work on their cars, well they got that. In a few cases, they got good service. In every case they paid a lot. What I am saying is, paying a knowledgeable professional (be it a mechanic, doctor, lawyer, plumber, or whatever) a reasonable fee to perform a quality service that will hold up, is a good choice compared to doing something, uhh, "half-cheeked", if you get my drift, and then having to pay not only for the original repair, but also to fix what you have done to the car. Or your plumbing, or body, or trying to fix something in court, etc.
Not disparaging your mechanical skill--you may be a whiz with a wrench. If so, ignore the above. However, if you were, I doubt you would be asking the kind of question you did where you did. If you feel comfortable working on your car, and want to take the risk, feel free. Get a good manual, and good tools, and I wish you luck. There are many people who do it successfully. But do be aware that someone familiar with cars in general, and your car in particular (EVERY model has its own quirks) can save you a lot of grief/money in the long run. Just my $0.02 Good luck, however you go.
PS--one of the reasons I work on computers now rather than cars is that the manufacturers have been making the cars more and more difficult to diagnose/work on for decades--not just wrench turning, but keeping the information needed away from the independent mechanics--and I just got fed up with it. If I have to trouble shoot a computer system in the dark, as far as information from the manufacturer goes, I would rather look on the web for stuff about Micro$oft than worry about the airbag blowing up in my face while trying to get the A/C to work.