I went to school and got my cosmetology license-and managed a salon for a few years.
Please DO NOT overprocess your hair and damage it! Do not jump the gun and go back for another perm...go the chemical straightening route, or start straightening your hair by using a straightening iron!!! This is only going to damage your hair!! I agree with what was said above, about letting the STYLIST judge if your hair can handle it or not. A lot of times stylists have to do processes that we KNOW will not turn out well-because the client won't listen to our warnings.
There are certain things a hairdresser can do to fix problems-but adding processing to processing usually only results in a lot of damage.
Yes, a perm WILL relax over time and not be QUITE as curly-even a god perm. Using a really good conditioner WILL help it look a little more relaxed, though. I also agree with only using the deep conditioner once a week or so...use regular every day, but use a GOOD one-as in, not Suave or V05.
If it is under $2...then that's not good.
I do stress though, that you should not turn to chemical processing to cover up a bad processing job-unless it is a terrible emergency as a last resort. You are only going to cause further problems. Also, while straightening naturally curly hair or normal hair for that "super straight look" with a straightening iron only causes minimal heat damage-doing this to freshly permed hair is a different story. Don't do it.
Chemically permed hair is basically "broken down" inside the hair shaft and shaped around the rod with the first processing solution. The second one neutralizes this process and "sets" it around the rod shape. You have basically just gone and broken down the natural configuration of your hair shaft with chemicals and reshaped it. If you take heat from a straightening iron and then "fry it flat" after chemically doing just the opposite-you are really going to damage it as well.