Jerry Joo, Lydia Mimiaga, Mina Manafi, Igor Marynowski,
Yes. Most likely you will experience some side effects, though some have had none.
Ho-Hum Reactions: Your body is agitated by the vaccine ingredients and your immune system is going to be working to produce antibodies to protect you against Covid-19. Everybody’s body will react differently, but the CDC lists some common side effects of your body’s antibody production efforts: These are common reactions to vaccines across the board, for all types of vaccines. It is also possible that you will feel no side effects. The CDC has printed a handout on this subject specifically for the Covid-19 vaccines which you can access here:
“If you have had a severe allergic reaction to any ingredient in an mRNA COVID-19 vaccine, you should not get either of the currently available mRNA COVID-19 vaccines. If you had a severe allergic reaction after getting the first dose of an mRNA COVID-19 vaccine, CDC recommends that you should NOT get the second dose.”
Other reactions like hives, difficulty breathing or swelling can develop within a few hours, but are unlikely. Don’t suffer in silence! Let your doctor know what’s going on! If you get your vaccine in a clinic or pharmacy, ask for their advice at the time of your vaccination. From footnote 3:
Precautions you can take:
Be prepared. If you have had side-effect problems with vaccines or other injections, you should consult with your doctor before being vaccinated. Carry on your person whatever drugs/pens, etc. you need to deal with any allergic reactions you have had previously from shots. Learn the difference between common (ho-hum) reactions and others.
Get your vaccination at a facility where personnel are trained to deal with severe reactions and have the equipment to do so on site. If you have doubts about this, go elsewhere.
Stay at the vaccination administering facility for at least 20 minutes before resuming your normal activities. This is common practice in the offices of allergists who administer allergy shots. Most reactions will occur in this time interval and by staying, you’ll be in the company of those who can render immediate care if a severe reaction develops.
Don’t minimize. If you have the slightest inkling that something unusual is happening to you, speak up! Let the medical personnel know.
Here is the CDC list of equipment (with people trained to use it) that Covid-19 vaccination sites should all have:
Some people should NOT get these mRNA vaccines without checking with their doctor first.
Those who have had bad reactions to previous vaccines should check with their doctor and follow the doctor’s advice.
Pre-existing conditions such as pregnancy, lactation, HIV, diabetes and immune disorders may introduce greater than average risk. If you are on immunotherapy, you should not simply show up at a vaccination site. Check with your doctor first. People in some of these groups were not part of vaccine trials in great enough numbers to draw conclusions and if you are among them, your risk is unknown.
Allergies to vaccine ingredients like some preservatives such as PEG will present whenever your body encounters those ingredients. Check out the vaccine ingredient lists (below for Pfizer & Moderna vaccines) and consult with your doctor before getting vaccinated.
“WHAT ARE THE INGREDIENTS IN THE PFIZER-BIONTECH COVID-19 VACCINE? The Pfizer-BioNTech COVID-19 Vaccine includes the following ingredients: mRNA, lipids ((4-hydroxybutyl)azanediyl)bis(hexane-6,1-diyl)bis(2-hexyldecanoate), 2 [(polyethylene glycol)-2000]-N,N-ditetradecylacetamide, 1,2-Distearoyl-sn-glycero-3- phosphocholine, and cholesterol), potassium chloride, monobasic potassium phosphate, sodium chloride, dibasic sodium phosphate dihydrate, and sucrose.”
“WHAT ARE THE INGREDIENTS IN THE MODERNA COVID-19 VACCINE? The Moderna COVID-19 Vaccine contains the following ingredients: messenger ribonucleic acid (mRNA), lipids (SM-102, polyethylene glycol [PEG] 2000 dimyristoyl glycerol [DMG], cholesterol, and 1,2-distearoyl-sn-glycero-3-phosphocholine [DSPC]), tromethamine, tromethamine hydrochloride, acetic acid, sodium acetate, and sucrose.
“WHO SHOULD NOT GET THE MODERNA COVID-19 VACCINE? [This goes for Pfizer, too]You should not get the Moderna COVID-19 [or Pfizer] Vaccine if you: • had a severe allergic reaction after a previous dose of this vaccine • had a severe allergic reaction to any ingredient of this vaccine 
Most of us should do just fine and tolerate these vaccines well.The disease itself is horrible for many and has unknown long-term consequences for those whose initial cases are in the “so what” category.
So what is the current state of development of other vaccines? The New York Times is keeping track of this info for you. Here’s a sample of the sort of thing you can learn at a glance on their site:
The information on the chart above is current as of 4 January 2021.