I am one of those who is allergic to blood worms. However, I need to feed them. I use frozen rather than freeze dried although many years ago I did use the dried. I have 20 tanks so I mostly buy the slabs of frozen food. However, I will only use bloods in the blister packs. I can pop these put and not touch them. The problem is that only reduces things.
I will still get itchy hands and eyes for a bit more often than mot. But by making sure i do not touch the bloods and then be carefull in defrosting and getting them into the tank. I can handle the milder and short term discomfort. I rinse off my hand s a lot during the food prep.
I believe I am allergic to something in the nitrogen complex. I am pretty sure it is nitrate. I discovered this decades ago before I even planned to keep fish. I used to develop B&W film and make prints. The chemicals in the various tray include nitrate I used to get 100s of awful tiny blisters all over my hands from this. Even holding a hand over the tray would do it. I next got this reactions from plant fertilizers. These often contain nitrate. It took me close to 20 years figure out the cause.
I now protect myself doing tank works with gloves. I am a right and I put a latex exam glove on my right hand and then seal it up with waterproof tape. I use a long sleeved aquarium glove (Aqua Gloves) on my left hand/arm. These gloves are fairly thick on one's fingers and make doing fine work with the left hand difficult, hence the exam glove on the right. I get by this way.
I agree with the possibility of likely needing to consult an allergist. What I would suggest is that you hide the bloodworms and do not open the jar or feed them for a while maybe a week or. If your symptoms lessen and then go away, you likely know what caused them. However, if your symptoms persist after starting this test fur a few days, see a doctor . If they get worse, do not wait, see a doctor sooner. You can even have your mom make an appointment for a week or so from now and if the symptoms stop, she can cancel it. However, I think you should discuss this all with her.
It is better to be safe and see a doctor needlessly than not to see one when you should. I am only telling you how blood worms affected me. This does not mean that is your problem. I am most certainly not a doctor.