I think that your best bet would be to see a dermatologist about your concern. You might also want to post your question in the WebMD Skin Problems & Treatments Community for more member and expert insight on your symptoms.
Here is a great article that may help in answering your question and give you some ideas of removing such dust and dander from your home.
According to the WebMD article , "Using a HEPA filter in your home can remove the majority of airborne particles that might be irritating or aggravate allergies. But the particles suspended in air are not the only ones in your home."
Make sure to check out the other methods of keeping your house a better place to breathe.
Unfortunately, I wasn't able to find any information on bruising from bug bites, but want to share this WebMD Slideshow on Identifying Bug Bites . Possibly you can find a similar bite in the photos to your own for some answers. If you have been itching the site, this may have also led to your bruising.
Please check out the WebMD Insect Sting Allergy Overview , though thankfully your reaction doesn't seem to fit this concern. If you find any other reactions, don't hesitate to call your doctor.
I'm not a medical professional and couldn't tell you if this is a food allergy, but definitely encourage you to read the Food Allergy Overview and speak with your physician and/or an allergist. Most food allergies tend to have more of a reaction than a sore throat such as itching, trouble breathing or swallowing, hives, diarrhea, etc.
The best bet is to always seek a medical professional for an examination and opinion.
If you are suffering from an allergic reaction, which is rare though possible , you should seek medical attention. Your doctor will be the best person to give you medical advice after an examination and help you with treatment. Please take care!
Unfortunately, no one here can tell you if you are or are not allergic to penicillin. Your best bet would be to seek an allergist for testing. Here is the WebMD Penicillin Allergy Overview for you to gather more information and speak with your doctor. Do stay safe and keep your doctor aware of your mother's concerns. I'm so sorry for her passing and wish you the best of health and happiness in the future.