How to improve hair density?

There is no way to do what you would like without causing further problem. You need to do nothing now and wait to see if you will have enough hair should you continue to have her loss to give a satisfactory result with surgery.I know of no product that will increase hair grows in the front of your scalp in more than 35 years experience doing hair loss surgery.   

You may want to speak to a qualified physician to see if you are experiencing male pattern baldness. If it is not possible for your hair to grow back, you may want to consider a hair transplant. 
At 20 years old, it would be important to plan for the long term by using the Shave Test to determine whether you will reach severe baldness and need body hair grafts, or whether you can rely on head hair alone. With a very short buzz cut style, Scalp micropigmentation techniques (like Trichopigmentation) can also create a natural looking appearance of density to reduce the visible areas of your scalp.
I have included a link below with more resources. 

I am sorry this has happened to you.  In my practice we often see patients who have signifiant loss in their 20s.  There are definitely options depending on the amount of loss and cause.  Often significant loss can be seen with stressful events or sickness and often will return over time.  If your loss is deemed to be androgenic in nature, the most important first step is to stop the loss.  This is best done with a combination of medications.  
Finally, in order to improve density your most effective options will be PRP injections with or without a transplant if you are deemed a candidate.  I would highly suggest you consult with a hair restoration specialist in order to determine your best plan. 

I'd recommend you see a dermatologist for a detailed scalp examination. Without seeing your scalp and knowing a lot more history, one can't make a diagnosis and offer treatment. But here's a few general comments for anyone with a similar story. 1.  Hair loss that occurs all over and not in one specific area is called diffuse hair loss. 2. Diffuse hair loss in men is not common, but causes include diffuse unpatterned androgenetic alopecia (DUPA), telogen effluvium, alopecia areata, lichen planopilaris and other scarring alopecias. The most common of these in a male age 20 with a diffuse reduction in density that then stops is telogen effluvium followed by diffuse androgenetic alopecia 3. The treatments for each of these conditions is different. 4. Many of these conditions do respond to treatment, including telogen effluvium and diffuse alopecia areata. Diffuse unpatterned androgenetic alopecia can most certainly respond to finasteride and minoxidil. Please take the time to get a proper diagnosis. Too often the assumption in men with diffuse hair loss is that the cause of hair loss is androgenetic alopecia and too often this is wrong. 

You should visit a hair
specialist to determine the type of baldness that has set in. If the hairfall
has stopped, then diagnosing the cause, improving your diet (protein intake);
medication in the form of multivitamins (Biotin) and PRP therapy (Plasma Rich
Platelet therapy) may help you to increase the density of hair.

I advice you consult a dermatologist who is experienced in hair loss.The first thing that must be done is eliminating dermatologic deceases that cause diffuse hair loss from typical male pattern baldness. If it happens that you have a dermatologic decease then early diagnosis and medical treatment may prevent you from losing more hair. Your hair loss seemingly being not active at the moment may make the diagnosis difficult, but it is still worth a close look as it may be activated again. If your hair loss is diagnosed as male pattern baldness, then you must seriously consider starting to take finasteride which will protect you from loosing a lot of hair very fast. 

I would schedule an appointment with a dermatologist. Options out there may be Finasteride and Minoxidil 5%.