From my reading of the literature, there is scant evidence that severity of reaction indicates a higher level of immunity.
Most folks do have at least some level of reaction; ranges from redness at injection site to fever and flu-like symptoms for a couple of days. This range of reactions indicates activation of the innate immune system, the system designed to eliminate foreign antigens, via activation of white blood cells (Neutrophils and macrophages).
Takes several weeks to achieve the full adaptive immune response through development of memory T and B-cells that will recognize the foreign antigen in the future (weeks, months, years).
The original Pfizer-BioNTech's COVID-19 vaccine trials (21,720 participants received the BNT162b2 vaccine and 21,728 participants received placebo), less than half of the participants reported systemic side effects (ie, symptoms other than injection site pain, swelling, redness), yet 95% protection against COVID-19 was achieved.
There is one study that suggest development of chills, tiredness, feeling unwell, or headache after the second dose are associated with higher neutralizing antibody (nAb) count at 6 months after the second dose. There are problems with this study, including it only measures nAbs, with no measure of cellular immunity (phagocytes, cytotoxic T-cells that target infected cells). There have been other similar studies that did not have the same findings, but the authors explain these away by study design differences (did not look out to 6 months, small sample sizes, etc).
