Is the immunotherapy a risky thing to do?

Benefit >risk. Immunotherapy can be risky in some settings. When done right by a board certified allergist in a controlled setting with a gradual build up risks are rare. Reactions can always occur as you are being injected with something to which you are allergic. That is why all shots are given in a doctors office with a doctor on site and all patients must wait 30 minutes after their injections.
There are risks. Immunotherapy has risks. Don't see a doctor who recommends & assures you that it's risk-free. You're injected with the stuff that makes you sick. Over time you develop tolerance. Reactions vary from mild redness & itching at the injection site (common) to hives or anaphylaxis (~1 in 1000 injections). Risk is greater if you have asthma. Competent nursing staff & waiting 30 minutes after help a lot.