Throughout my experiences, this is what I have come across.  Most people have these questions about the side effects of waxing, why does it happen and what should they do.  Listed below are some information that might help you better understand the side effects of waxing.

Just know that waxing will have some side effects regardless of skin type and skin area.
No need to worry.  These are normal as long as you follow the proper after care routine.

1. Redness
Because of the heat from the wax the blood vessels will dilate which will create more blood flow into the area being waxed.  This happens because the body reacts to the follicle being pulled out from the root.  Applying an aloe-based serum to the area will help calm the skin.

2. Pimples
Unfortunately, there is a chance this will happen no matter where you go and even if you're not prone to acne.  Waxing opens the pore leaving it exposed.  The pimple can form if the pore becomes infected with bacteria.  Popping or picking at them spreads the bacteria and can encourage even more pimples to appear.
Try using an exfoliant with salicylic acid which can both prevent pimples and treats them.  You can also try tea tree oil to the area to treat the pimple.

3. Ingrown Hairs
Sometimes after the hair has been removed, it regrows downwards instead and doesn't break the skin's surface.  This is more common in areas where the hair is thicker such as the underarms and bikini, and occurs more frequently in people with curly hair.
Try to exfoliate 24 hours prior to and after waxing three times a week then follow up with an ingrown hair serum.

4. Bumps
Similar to the razor burn, raised bumps are often caused because of the body's reaction to the hair follicle that's being waxed and stress that occurs on skin.  Bumps that appear without redness oftentimes last for 2 days and disappear afterward so no need to treat them.  
There are some topical cortisone creams to reduce inflammation.  I suggest using aloe or tea tree oil if the bumps don't go away after a few days to decrease infection.  You can also use a cold compress to soothe the skin.

5. Bruising
Common for sensitive skin since the skin is held taut or with the tugging and the pulling as we wax.  You can apply a cold compress.  The cold temperature from an ice pack makes the blood in that area flow more slowly. It may reduce the amount of blood that leaks out of your vessels.

6. Burned or removed skin
Because the skin is being waxed on the same area more than once.  This could also be from the medications you are taking, skin care products or a medical condition.
Retinol can make the skin thinner and prone to lifting during a wax.

People that are prone to this are:

(the main issue is the potential for reduced wound healing ability, which can mean you are more susceptible to infection and you lack sensations on your skin; any injury to the skin caused by waxing is therefore a concern)

- people taking ANTIBIOTICS 
(it causes skin to be very sensitive this is why sun exposure while on them is a bad idea and topical antibiotics which are usually taken for acne or fine lines, wrinkles, and rosacea exfoliates the skin too)

- during your menstrual cycle
- pregnancy
- ACNE MEDICATIONS (Accutane, Retinol, Retin-A, Tretinion, & Alpha Hydroxy Acid)
I suggest applying some antibacterial cream or Aquaphor for barrier on the skin.
You can also use Neosporin on the burned skin and avoid any heat as much as possible until it's healed.

7. Pain
May only be present while the hair is being removed but can be hard to deal with on delicate areas.  Take some tylenol an hour before to reduce inflammation and help alleviate pain during and afterwards.

8. Hives/Histamine
A histamine reaction is easily identified by a rash that presents itself as welts or bumps.  This may happen immediately after waxing and may last a couple minutes, hours, or a day depending on the person.  
Histamine works by enlarging the blood vessels and making them easier to penetrate.  The body then swells and protects the affected area.  This reaction is normal.  At the end of the day, waxing means pulling a good amount of hair from the root all at once, multiples times.  The skin has every right to protect itself with these responses.  Since waxing causes a type of trauma to the skin, the body responds to this trauma by releasing histamine.   Try applying a cold compress to calm the irritation or you can try taking an antihistamine.

9. Post-wax Rash
Usually subsides on its own in a few days, however if there's pus forming or there's an infected ingrown hair, which may happen even a week after waxing, get it checked by a dermatologist.
Results in a mild trauma to the skin that the follicles are exposed to from the pulling.  They are fairly common and usually subsides on its own in a few days.  If there's rashes every time, waxing may not be for you. 
Apply a cold compress, wear loose-fitting clothes, apply cortisone based cream to reduce swelling, or take some antihistamine.

10. Folliculitis
Appearance is similar to rash, pimples and bumpy.  This is caused by inflammation that normally recedes on its own in a few days.  There is white bumps filled with pus/cyst due to ingrown hair. Infection may occur because hair follicles gets infected by staph bacteria, which are usually present on the skin.

11. Mild burning sensation/itching
Both these reactions are related to redness or bumps.  They are a form of irritation and the body's way to respond to the external threat of follicle pulling.

12. Contact dermatitis
This causes a rash after waxing.  Common to people with sensitive skin, waxed used or chemicals and fragrances from soaps and detergents.  They are itchy, painful to touch, burning, or stinging feeling on the skin.

14. Spot bleeding
Should be minimal, just a couple pores, and mostly if the area you have waxed is very sensitive.

15. Hyperpigmentation 
If your skin looks darker, kind of like a sun spot is forming, your skin may be extra sensitive to the sun or reacting to a medication you're taking.  This takes time and patience to treat.
Ask your dermatologist to prescribe you a hydroquinone which is a skin-bleaching agent that can lighten dark patches on your skin.  Also ask your dermatologist about products with niacimide or mandelic agent in the ingredients to help with hyperpigmentation.