Hi Carl,
I've been type 1 for 27 years, and in this time I rarely had in problems with colds and flu. About 6 years back I had flu which confined me to bed for a week, wasn't well at all, but apart from that nothing much really.
Like Kegstore, I get the seasonal flu jab each year, which is recommended for diabetics regardless of type. I have been told that we are supposedly susceptible to colds and flu, I know from when I had flu it certainly caused problems with my blood sugars, so be careful to monitor your bg's whilst unwell.
I am a great believer that your diet can have a influence in your well-being. Should you eat a well balanced diet of fruit and vegetables, this can play a role in fighting viruses and infections. I also take a Vitamin C tablet daily, which is supposedly helpful in fighting colds and flu. I don't know much about cold remedies like lemsip etc doing any good, as you say they are probably full of sugar, don't know if they do a sugar free version, I normally like to ride it out, but if you are unsure ask your pharmacist or gp for advice.
Regards
Nigel