The colds and flu are almost certainly down to not drying the nostrils as this is one of the reasons I was trained to dry my nostrils. My training was provided in a yoga ashram environment, and drying of the nostrils is important to help prevent problems like this occuring. People who have excessive nose bleeds should seek expert advice before even thinking of doing Jala Neti. The following webpage explains how to dry the nose: http://www.jalanetipot.com/how_drying.html
I would suggest a few things, one start using a neti pot, and maybe go to some one who has been trained fully. It might be worth stopping the practice you currently do for a month or so and see how things turn out. Maybe resuming a jala neti style practice. I practice jala neti daily and have no problems only benefits, but I dry my nostrils and then do an asana practice afterwards. The asana practice afterwards (espeically if inverted postures are used) would help drain any water left in the nostrils, but for me this rarly happens because im so good at drying the nostrils.
I would suggest researching Jala Neti some more, and ideally going to a yoga teacher or ashram to be guided in the practice. The following books discuss Jala Neti (and of course there may be others.
Page 15 of the Yoga and Kriya (Swami Satyananda Saraswati)
Page 203 of the Hatha Yoga Pradipika
The neti pot I use is; http://www.yogameditation.com/products/nosebuddy
and it comes with some excellent instructions. Jali Neti is one of the Shatkarmas (6 cleansing practices) and they are meant to help not hinder progress, and thats why I suggested you stop practicing for a short time to give the body a time to dry the nostrils and for any lasting effects to go away. It will also give you a clearer idea of how you are like when you don’t practice, a usefull contrast for personal education.
The practice of Nadhi Shodhana (alternate nostril breathing) can also help clear and clean the nostrils, so you could try this for the duration of time you take a break from the practice, assuming you want to do both.
With what ever you choose to do, I wish you the best, having poor health is obviously not nice.
Om Shanti Shanti Shanti
P.S. It’s a shame the topic has fragmented into a PM now, I would be interested in the key points discussed.