First of all, who prescribed you Luvox and why that particular drug? A psychiatrist or a regular doc? As for anti-depressants, they are usually quite small so it's hard to see even a person with the most difficult problem swallowing pills would have a problem with them. There are liquid versions of most of the ssris and snris because they're very hard to stop taking and using a liquid helps taper them down very slowly. They don't taste great, but there are liquid versions. But again, these pills are pretty small.
I would imagine that chewing them would taste horrible. Please talk to your doctor---- take the medication exactly a they tell you. If you need an alternative for whatever reason do to issues taking it whether liquid form or something else, talk to your doctor about it. Good luck!