I’ve had both. The pneumonia vaccine gave me a sore, achy arm for a few days, but it wore off.
I had more reaction to the shingles vaccination (given in 2 doses, 6 months apart). The first dose was worse in terms of side effects with a swollen arm to the elbow for about 36 hours, plus nausea and chills. The second dose, my arm was sore but not swollen for a day and I experienced nausea and chills overnight, but it soon wore off. I took paracetamol to help.
I consider those side effects preferable to the alternative.
However, I don’t know if things would have been worse if I was immuno-suppressed. Perhaps have a word with the doctor/nurse at your GP practice if you are concerned, and then go by their advice.