This has been discussed several times in the wet canvas forums. Don't worry so much about paints. If it was such a serious/immediate risk, myriads of painters in this forum would be seriously ill and the paints forbidden forever. Yes, one has to be careful, avoiding to do it all the time, however the quantity of harm substances isn't big that's why we are allowed to use them, taking precautions of course. Low cost paints contain even less cadmium than expansive ones
Fumes from a tube are a small quantity. In case of some big can of 1 liter it could be else. I think solvents for oil colors are worse for much more people.
If this is the first time you use acrylics, you can look if you are somehow sensitive to their ingredients. Cadmium or titanium aren't the only harmful ingredients in the colors. There are other chemicals too, in much more quantities. If so, you have perhaps to avoid contact to acrylics, not just to smell them.
It is probable that your nose problem is due to some allergy, something usual in spring. Myself, I had nothing like this as a youngster, but now I have similar problems almost every winter & spring (I don't use oils or acrylics these late years, just colored pencils, watercolors and legacy graphite pencils).