Yep.
The 'aches' following immunizations and during illnesses are actually caused by our immune system.
White Blood Cells (of all their different types) are made in one of 2 main areas. Our bones (b-cells), and thymus (t-cells). Antibodies are distributed via our lymph system (lymph nodes, and the space between cells and a big ole tract through our chest). Lymph nodes swell when we're sick, particularly at our throat and groin as they're churning and flushing our lymphatic system.
Between our bones aching from manufacturing b-cells, and our lymphatic system running at max capacity... Our bodies can really HURT when we're sick (and the sicker we are, the harder our system is working, the more things hurt as a general rule, our immune system doesn't give a rip about pain when it's manufacturing armies in the hundreds of millions).
Certain infections are known to cause certain very specific immune responses (Mumps, Lyme. Rheumatoid, Etc.), but the aches are pretty normal for even the common cold, and many people feel them more in one area than another. I feel it in my knees and hips, my son in his arms, my mum in her hips and back.
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A little known trick outside of medical land is McDonalds. Antibodies and WBCs are made almost entirely out of fat with just a little protein thrown in for structure. The same things that made fast food bad for us when we're healthy make it GOOD for us when we're sick: high fat content, broken down/processed so much as to already be mostly digested. Chicken soup for the same reason (fats and broken down). But fast food has more fat in it. Anyhow, a high fat diet when you're sick supports your immune system and lessens a lot of the effects you feel (like bone and joint pain). Ditto, simple sugars for your brain and nervous system.