It sounds like you are interested in the "Quantified self" movement, which deals with self knowledge about one's body function. While this is not a comprehensive answer, there are a few things to consider:
1) Many hormone levels follow diurnal (24hr) cyclical patterns, and vary throughout the day. Sleep schedule (wake/bedtime) affects these cycles. This taking single measurements at different times of the day would give you very different results.
An example of sleep pattern (black bar is sleep relative to 24 hr time), wake up times would affect hormone levels at different times.
2) There are seasonal variations in hormone levels (for example these control white/brown fur color in animals living around arctic circle). As such, your 3 month study needs to account for the change in seasons, and may be heavily influenced by natural changes.
3)There were a number of startups trying to sell hormone testing kits like this one to general public, however these are expensive and "not intended to treat, diagnose, etc". In short, without your own lab, it's really hard for an average person to get this kind of info. A doctor can prescribe a single time test, but those can easily cost hundreds of dollars and are not very descriptive, as the "normal" ranges they give are ridiculously broad (for example testosterone is at range 270 to 1070ng/dl)
4) While it's common to hear popular science refer to "serotonin or dopamine flooding the brain" - ask yourself, where is this flooding occurs? As such, where do you actually measure these changes? I still can't find a clear answer to these questions.
My personal research into sleep makes me hypothesize that one can get an impression that something is changing in the serotonin/dopamine/testosterone system by looking at the duration, clarity and content of one's dreams.