Can proteomics be used to predict if vaccines will result in health complications, allergies, etc?

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Brief answer to your question:

"no." Although proteomics is used to search for antigens suitable for creating new vaccines.

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Proteomics is a field of molecular biology dedicated to the identification and quantification of proteins (in other words, high-performance protein research). The term "proteomics" was proposed in 1997[1]. The totality of all proteins in a cell is called a proteome[2].

The object of proteomics is proteoms that are expressed in a given cell, tissue, or organism at a given time (i.e. proteome). Though the first methods of proteomics, for example, sequencing of proteins according to Edman, appeared long before genomic technologies, really high productive studying of proteins became possible only in post-genomic epoch, i.e. at presence of known nucleotide sequences of genomes of different organisms.

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With MALDI-TOF it is possible to determine pathogens with precision to births and species. Contact bacterial cells are applied to a metal target of a mass spectrometer, covered with a matrix, irradiated with a laser, and specific profiles are obtained which are recognized by a trained algorithm by characteristic masses[46].

The possibility of using proteomics to diagnose cancers by analyzing protein biomarkers as well as determining the degree of malignancy of the tumor is investigated. Some success has already been achieved in this direction. For example, in the USA it is allowed to use the Xpresys Lung test developed in 2015, which uses targeting mass spectrometry of several plasma proteins and evaluates the degree of malignancy of tumor nodes in the lungs[47].

The latest advances in proteomics - in mass spectrometry and in the separation of organelles and membrane proteins - can make it possible to study the heart proteome and identify the modified proteins (and determine the nature of their modification). Heart proteome data will help to understand the mechanisms of various cardiovascular diseases[48].

Many drugs are either proteins themselves or act on certain proteins. This is why proteomics has been adopted by specialists in drug development[en]. Most pharmaceutical companies have a proteomics unit or partner company that specialises in proteomics. Proteomics methods are used to confirm the validity of the targets of the drugs being developed, to determine the effectiveness of biomarkers, to study the mechanism of action of the drug and its toxicity. In particular, proteomics methods are used to search for antimalarial drugs[en] that bind to purine-binding proteins at the stage of plasmodic reproduction in erythrocytes and their release into the blood[48].

Comparison of proteoms of two organisms (not necessarily closely related) allows to reveal both proteins common to these two organisms and proteins that cause differences in their phenotypes. Such an analysis can provide information useful for understanding the evolutionary process[49] and sometimes allows to identify previously unknown protein functions. For example, with the help of comparative proteomics the proteins of insect Nilaparvata lugens[en], involved in the processes related to reproduction, whose expression changes in response to insecticide treatment, have been detected[50].

https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%82%D0%B5%D0%BE%D0%BC%D0%B8%D0%BA%D0%B0

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Proteomics is the large-scale study of proteins.[1][2] Proteins are vital parts of living organisms, with many functions. The word proteome is a portmanteau of protein and genome, and was coined by Marc Wilkins in 1994 while he was a Ph.D. student at Macquarie University.[3] Macquarie University also founded the first dedicated proteomics laboratory in 1995.[4][5]

The proteome is the entire set of proteins that is produced or modified by an organism or system. Proteomics has enabled the identification of ever increasing numbers of protein. This varies with time and distinct requirements, or stresses, that a cell or organism undergoes.[6] Proteomics is an interdisciplinary domain that has benefitted greatly from the genetic information of various genome projects, including the Human Genome Project.[7] It covers the exploration of proteomes from the overall level of protein composition, structure, and activity. It is an important component of functional genomics.

Proteomics generally refers to the large-scale experimental analysis of proteins and proteomes, but often is used specifically to refer to protein purification and mass spectrometry.

https://en.wikipedia.org/wiki/Proteomics

If vaccines have side effect.