Both my husband and I have environmental allergies, but no food allergies other than my husband's childhood lactose intolerance, which isn't a true allergy.
My 15 month old ingested peanut butter and had hives, so we had him tested both with the skin prick test and with the RAST test to see if he also had tree nut allergies as well as to gauge his likelihood of reaction, something the RAST can tell you and then you can retest later on to see if the reactivity is going up or down.
I was surprised to find that in addition to a life-threatening peanut allergy, he has an allergy to dust mites and cats. We have cats! He hasn't really had bad symptoms other than some eczema as a baby and occasionally a sniffly nose. But I'm really glad that I found out because left untreated and given his allergenic predisposition, he's at higher risk of developing asthma. Now that we know, we are electing to give our cats away (sad about this but it's for the best in our situation). And we bought protective coverings for our mattresses and pillows to ward off the dust mites. We'll also vacuum much more diligently now.
The doctor also put him on Zyrtec. He said that there's some research indicating that it may prevent the onset of asthma if taken as a young child. Since he's at risk, we've put him on that.
All of these preventative measures may help prevent a serious illness... and knowing exactly what to do regarding his food allergy was comforting. Your allergist won't necessarily recommend shots I'd think, especially at this young age. They may just have you take certain precautions with your baby.
I don't have a lot of info regarding the vaxing. We've vaxed on schedule so far but I've treaded a little bit more carefully since my son's skin test. He had a very very small reaction to egg. He's never had any reactions when he's had egg in things that I can tell but some vaccines do contain egg. I have read that the MMR isn't supposed to be problematic for those with allergy to egg, but if you had a very sensitive child I imagine you might have some concern. The flu vax contains egg I believe.
I have no idea what is in allergy shots. That would be something to read up on.
I was afraid that my 15 month old would have a lot of pain from the skin test but he barely made a peep, and when they drew blood for the RAST he didn't even cry, he just stared at the nurses who were cooing at him. I think I was more traumatized than anyone.
Some allergies won't develop yet, and some may be outgrown, but I don't see why it would be a bad thing to have him tested if you are anxious about it. If the allergist thinks it's not a good idea they'd hopefully tell you to wait.
Since you do have a history of allergies in your family I'm assuming you're not giving your baby foods from the groups that tend to give serious problems. I'm pregnant and the doctor advised me that given my son's allergies, we should avoid milk until age 1, eggs until age 2, and peanuts until age 3.
I hope this helps a bit!