I'm afraid of chemicals. How do I handle my required uni biology class?

To further echo one of the comments:

Seek professional help. This may be a trained psychologist, or even just a general medical practitioner, who may be able to direct you to another institution if necessary. You may have access to mental healthcare through your institution if you do not otherwise have access. Specific phobias are treatable. Formally addressing this will do two things for you:

• It may or may not help you overcome your fear. This may not be necessary just because of a single bio class alone, but it sounds like your condition is limiting your life in other ways, and this just may be a good trigger for you to seek a treatment that may improve your life in general going forward.
• However, even if the treatment is not successful, or takes too long to help you much with your class (treating phobias can be a long-term project, from my limited understanding), your condition is now on record, which allows you to approach whatever office in your university is responsible for handling special needs students. They should be able to convince the teacher to find alternative ways for you to do the class without handling chemicals, but they will almost certainly not act unless you have documentation from a qualified medical professional.

_{(This answer supposed the OP is an American; which turns out to be true, but they are attending school in Canada, so while the general thrust of the answer remains valid some of the US-specific aspects are obviously not immediately relevant)}

Phobias can potentially fall under mental disabilities, which may then subsequently be covered and protected by the Americans with Disabilities Act (this would be determined by the particulars of your case). I suggest contacting your university's disability office for help and guidance.

I realize that rational arguments do not help phobias. Dealing with a phobia will require therapy as suggested by the other answers.

Sometimes understanding better the things you fear can help you cope with the fear. Sometimes not. If this is a case where understanding might help, you should realize that pretty much everything is a chemical (the only tangible exception I can think of is light). You are made of many different chemicals (water, salts, sugars, fats, minerals, polypeptides, polynucleotides). Everything you touch, eat, smell, and taste is made up of chemicals. You might argue: "Sure, but those are natural chemicals. I have a fear of artificial chemicals." My response to this is that natural and artificial have no clear definitions. Many chemicals made industrially can be found in nature and in living things. Many natural compounds (including things you can find in the woods, such as mushrooms) can be as hazardous as any cleaning agents that you have. The most toxic compound (in nanograms of toxin per kilogram of body weight), botulinum toxin, is natural.

An important guideline in toxicology is: the dose makes the poison. For instance, carbon monoxide and hydrogen sulfide are well-known to be "toxic chemicals" and exposure can be fatal. However, your body produces both of these chemicals in small quantities as a normal part of metabolism. Despite its toxicity in relatively large doses, your body produces hydrogen sulfide to send signals and it plays an important role in blood flow. Your body is perfectly capable of detoxifying small amounts of many "toxic" compounds and does this all the time as a normal part of metabolism.

Since you are interested in science, I heartily recommend that you study chemistry and toxicology. This will allow you to better understand the risks and nuances of toxic substances.