The incubation for Hepatitis A is on average 25-30 days- it takes this long for symptoms to develop. So if you are housemates with patients with Hepatitis A, you could indeed already be incubating the virus- either from having contracted it from them, or from acquiring it the same place they did.
There have been several studies now that show a benefit in vaccination as "post-exposure " prophylaxis. Giving you the vaccine now, will be as effective as giving immune globulin, but it also will provide long term protection ( if you complete the vaccine series of 2 shots).
The immune globulin is a blood product- with low risk of side effects/ contracting infection, but would only give you short term protection.
As far as testing- I am not sure you may have understood ( or they may have misspoken) - Testing for Hepatitis A antibodies will get a result back within a couple hours- but this will just check if you ALREADY have protection. If you check a Hepatitis A total antibody, and it's positive, you already have pre-existing protection and nothing more needs to be done. If you do not have pre-existing antibodies, then as I noted above it can take 1-2 months for the incubating infection ( if you are infected) to show up- and you should have post-exposure vaccine or immune globulin now to prevent it.
If I saw you- I would consider checking hep A Total antibody and then vaccinate if negative ( and do nothing if positive). But I would give vaccine over immune globulin. Alternatively, one could consider just vaccinating and not testing, if you have been at low risk of prior infection.
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POSITIVE feedback & a BONUS are warmly appreciated. Please note that answers are for information only, do not take the place of an IN PERSON assessment by your doctor,and does not establish a patient-physician relationship.