Anaphylactic reactions may be more likely with mRNA COVID-19 vaccines than other traditional vaccines (1 in 100,000 vs. 1 in 1,000,000); likely a reaction to carrier used to protect RNA component (polyethylene glycol, PEG), rather than the vaccine per se.
https://www.nejm.org/doi/full/10.1056/NEJMra2035343?query=featured_coronavirus

Persons with a history of allergic reactions associated with polyethylene glycol (or reactions to any of the other components listed) should avoid mRNA vaccines, and receive a different type of vaccine instead.

Note that other kinds of allergies (e.g., hay fever), are not expected to cause a problem.

There is no need to avoid the mRNA vaccines unless there is a specific history of allergic reactions to polyethylene glycol, or the other ingredients of the vaccines.

The risk of an anaphylactic reaction remains extremely low at 1 in 100,000.

These are good odds!