Lymph nodes are organs as they are made up of lymphoid tisssue. They are part of the lymphatic system. Similarly, the heart is an organ as it is made up of different tissues such as muscle and nervous.
Swollen lymph nodes are something that should be felt by doctors and diagnosed. You should not go and press them. It is difficult for me to describe how it feels. Also different causes of swollen lymph nodes can result in different swelling : the extent of swelling and whether it is localised or widespread.
I am going to make a general statement that swollen lymph nodes are above 3cm.
Please ignore your symptoms and see your doctor please.
Lymph nodes can be palpable. It is just a normal organ.
Go see your doctor.
Talk to your doctor. Highly unlikely you are seroconverting and a pimple-like lesion on the back of your neck has nothing to do with HIV.