in my first year of flying i had so many sick days i was crying too!
i had encountered the tiredness thing with previous jobs so i was ok with that because i was sort of used to it but oh my god, the amount of sick leave i had when i first started!!!!
at one point (due to continual ear infections) people were telling me that 'mabye flying is not for you" and that was upsetting becuase i didnt want to give it up.
i have since found out that quite a high percentage of people get quite sick in their first year of flying.. after about 9 months to a year you will notice it will pass. its your body being exposed to all those germy people in the cabin and having everything recycled through the cabin so you are continually getting sick. your body will become immune soon and it will be ok.
You should however try to get as much sleep as possible, eat well and take some additional vitamins. i found that drinking a berocca each day really helped in the long run, not only was it a great pick me up but that one little berocca each day gives you alot more minerals and things that your body could be needing and about a week after taking them you feel alot better and healthier. good luck!