The VAERS (Vaccine Adverse Event Reporting System) is a publicly available USA government searchable database for (as the name suggests) reporting vaccine adverse events. The actual searchable part is known as CDC Wonder and is available from the VAERS Data Page. It is fully capable of giving you data directly on the adverse events associated with vaccine lot. The answer from @BipedalJoe is an aggregator that queries the CDC and provides summaries of some of this data.
It should be noted that VAERS comes with some very important caveats; in particular those noted in the disclaimer you will need to click "I have read and understand" to get past when accessing the data. I have reproduced it here, with my own emphasis:
VAERS accepts reports of adverse events that occur following vaccination. Anyone, including healthcare providers, vaccine manufacturers, and the public, can submit reports to the system. While very important in monitoring vaccine safety, VAERS reports alone cannot be used to determine if a vaccine caused or contributed to an adverse event or illness. Vaccine providers are encouraged to report any clinically significant health problem following vaccination to VAERS even if they are not sure if the vaccine was the cause. In some situations, reporting to VAERS is required of healthcare providers and vaccine manufacturers.
VAERS reports may contain information that is incomplete, inaccurate, coincidental, or unverifiable. Reports to VAERS can also be biased. As a result, there are limitations on how the data can be used scientifically. Data from VAERS reports should always be interpreted with these limitations in mind.
It is also important to note that many healthcare providers are required to provide reports to VAERS of ANY event following vaccination, whether it may be related to the vaccination or not. For this reason, you get reports of things like car crashes on icy roads in VAERS. You should also be aware of some answers I have made on similar topics over the past couple of years, which might be of relevance: Does covid vaccine have a ratio of 1:718 of adverse events?, Are vaccinated people more or less healthy after vaccination?, How bad are covid vaccines?.
In a comment @BryanKrause provided a link to an news article published in the journal Science 1, which provides an excellent overview of some more of the issues associated with VAERS data and common problems in interpretation of the data. I've mentioned the problems covered in the disclaimer, but another serious issue is interpretation of the results. To quote the article:
People may misinterpret VAERS, which is easily searchable, as a catalog of actual side effects, rather than possible or suspected ones.
This means that just because VAERS has a report, that it is a causal relationship between the event and vaccination. Known causal side effects of the vaccines are included in the datasheet provided with the vaccines. I believe that the supply of this information is mandated by law in many countries for any therapeutic or prophylactic, and is supplied with the actual vials. You should be able to ask your vaccination supplier for it and/or search these online.
Anyway, on to the question at hand:
Within the CDC Wonder page you can change the "group by" selection box in the first section and ask to group by "vaccine lot":
In the second section, you can select specific symptoms if you wish.
The 3rd section is more relevant - it is the one for the type and manufacturer, as well as dose, choose the one(s) you want. You can also select a particular lot if you know this information. See the box, bottom right:
Sections 4-11 allow you to select locations, event characteristics (type of injury for example), vaccination date, adverse event date, death rate etc, if you are interested.
Section 12 allows you to access/see the data, including in a downloadable format.
- Wadman M., Antivaccine activists use a government database on side effects to scare the public. 06 May 2021. doi: https://doi.org/10.1126/science.abj6981