We definitely had a lot of coughs/colds/virus/gastro and even chicken-pox in the first year of arriving, and I had a whole round of them again (well, not the chicken pox) when I started working in a childcare centre.
The dry air makes it easier for viruses/bacteria to get through your body's defence system, plus you are in a new place with new diseases that your body has no immunity. Double that with a long plane journey in a confined space with dry air, the jet lag, and the sheer exhaustion of packing up your old life and starting something new...
I recommend you familiarise yourself with your local medical centre, pharmacy, and get plenty of rest, water, sunshine and fresh air...
With the sore throat, 'strep' throat is very common here (well, certainly my colleagues and I seem to get it a lot) - it's caused by a bacteria, makes a very very sore throat, and you need antibiotics by around 48 hours - I had it and by the third day I was having trouble swallowing water...you can easily end up in hospital needing rehydration and IV antibiotics.
To test for it, they will do a swab at the back of your throat (painless and simple) and be able to run the pathology very quickly...
Going to the doctor is not that expensive...between 40-80chf. In Australia we pay $40, so not much difference - it's the medications that are very expensive compared to what I am used to paying.
We budget 50chf a month for the kids to cover their 10% franchise, and at least 100-200chf a month for medical expenses for my husband and I - for the first 3 years I managed to pretty much avoid the doctor except for things that aren't covered anyway, but am just about to change to the lowest franchise because I really need to start considering my health and wellbeing more...
I think at some point you have to consider your health valuable, and be prepared to pay the costs for the sake of your wellbeing - a colleague of mine avoided the doctor all year, and was sick several weeks and couldn't do her job very well, and ended up quitting her job and having a stint in hospital...from the outside looking in, to spend those 100-200chf a month would have been a much better investment...