Kind of hard to advise residing the whole house without seeing the siding. There are many reasons why your house is leaking, and it is hard to tell without looking at it.
Don't, and I repeat don't apply a marine sealant. The person that suggested this is flat wrong. Most marine sealants are not designed for a southern exposure.
My strongest recommendation would be for you to reside the south side only, if there are budget limitations. The south side usually fails before the rest of the house due to the heating and cooling extremes of the sun.
With respect to caulking, it you caulk, I'd recommend using a sealant, not an adhesive. Based on your questions, I'd advise you contact a local contractor, let them know you can't afford to reside the whole house, but you have a problem on the south side.
If you wait, the likelihood of the wall rotting inside is great, and this will get costly, so waiting isn't free, either.
I'll also advise you expect to work with your contractor because they might find something more than we can here on the fixitforem.