Can mono cause alopecia?

Alopecia areata is an autoimmune disease. Environmental factors play a role in many patients to trigger the disease in patients who have the correct genetic predisposition to the disease. 
Studies have examined whether environmental factors like stress, as well as various infections play a role in alopecia areata.
Epstein Barr Virus (EBV) is the virus known to cause mononucleosis. A 2008 study examined whether mononucleosis could be a trigger for alopecia areata. The study examined
6256 individuals. 1586 patients reported an environmental trigger-including 12 individuals who had an EBV infection within 6 months before the onset of AA.
The role of EBV and mononucleosis is not proven definitively but there is some evidence that it could be a trigger for a small proportion of individuals. More studies are needed.
As far as how to treat your specific situation- I would need more information. A variety of options are available including steroid injections, DPCp, anthralin, platelet rich plasma, oral sulfasalazine, oral methotrexate and oral tofacitinib. Please see a dermatologist for evaluation and discussion.
Reference
Rodriguez TA, et al.Onset of alopecia areata after Epstein-Barr virus infectious mononucleosis. J Am Acad Dermatol. 2008.

You likely have scarring alopecia which is a an umbrella of hair loss disorders that affect about the 3% of hair loss patients.The cause of scarring alopecia remains unknown. Health experts are divided over the reason why this condition occurs. However, scientists agree that inflammation is the key factor that causes the destruction of hair follicles, stem cells, and sebaceous gland. When the stem cells and sebaceous gland are destroyed, the hair follicles will not grow back. This condition is neither contagious nor passed through genetics.
Your doctor will likely prescribe anti-inflammatory medications including hydroxychloroquine, doxycycline, mycophenolate mofetil and corticosteroids. Topical corticosteroid creams may also be prescribed. For alopecia caused by certain pathogens, oral antibiotics and isotretinoin are usually prescribed to keep hair loss at a minimum.
Once the symptoms stopped, your doctor could also stop the treatment. However, scarring alopecia tends to come and go. It will have periods of remission and reactivation throughout your lifetime.
Do note that some alopecia meds cause certain side effects. As such, consult with your doctor about the potential effects of the medication. Also, note that the meds are not meant to restore hair follicles. They are only taken to reduce inflammation. This means these drugs will not restore hair growth nor promote re-growth. Once the hair follicles are destroyed, they are typically destroyed for good.

Illness can cause alopecia by the stress of the process. As you are geoing treated by a dermatologist, there is little I can offer you here