See here.

A common misconception is that mRNA vaccines represent a new vaccine platform developed to combat COVID-19. Whereas, mRNA vaccines have been designed and developed for years against other pathogens, such as ebola, zika, rabies, influenza, and cytomegalovirus [22, 23].

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Although the COVID-19 vaccines made by Pfizer/BioNTech are the first mRNA vaccines to complete all clinical trial stages and be licensed for use, the technology has been around for a while.

Human trials of cancer vaccines using the same mRNA technology have been taking place since at least 2011. ‘If there was a real problem with the technology, we’d have seen it before now for sure,’ said Prof. Goldman.

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Although there are no previously approved mRNA vaccines, these vaccines have been trialed in humans for oncologic therapies for nearly a decade (NCT01684241), and have been trialed in humans for infectious disease for over 3 years.6 Regarding adverse events, data from phase I influenza mRNA vaccine and phase III COVID-19 mRNA vaccine trials have demonstrated that injection site pain, erythema, swelling, fever, fatigue, headache, chills, muscle pain, and arthralgia are more common in the vaccine group relative to placebo.3 , 4 , 6 These events are consistent with reactogenicity, which is expected after immune system instigation.

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Another concern expressed by some is that the development and FDA review of the vaccines occurred too quickly for the vaccines to be adequately vetted. The development and review of these vaccines has been undeniably fast. The rapid development of the vaccines was possible due to the nature of mRNA vaccine production and the many years of preclinical and clinical development. All that is required for development is knowledge of the sequence of the antigen, in this case, the SARS-CoV-2 spike protein. Following their development, these vaccines underwent the same FDA review steps that all drugs are required to go through. The review process was quicker than normal due to the urgency of this pandemic. No steps were omitted in this process.

All this also misses one point: the J&J vaccine is viral vector. This technology is well well established and doesn't use the mRNA platform. If you're worried about it, get the J&J shot.