If I got infected once from Covid-19, will I develop immunity?

We don’t know if infection with the novel coronavirus confers long-lasting immunity. If it does, then something similar will happen: Eventually, almost all adults will be immune, and new infections will be concentrated among children. Since the virus causes severe disease almost exclusively in older adults, this shift to a childhood infection would nearly, but not completely, eliminate hospitalizations and deaths from the virus

But none of the coronaviruses currently common in human populations confer lifelong immunity, and there is a very good chance that SARS-CoV-2 won’t, either. Still, subsequent infections with the virus will almost certainly be less severe than the first, as individuals accumulate partial immunity. This is similar to the incomplete protection you get when the flu vaccine is an imperfect match for circulating strains; you can still be infected, but the resulting illness is far less harsh. This partial immunity would have a similar, if less dramatic, effect on the age distribution of the disease, reducing illness and deaths in older adults.

Sources: https://github.com/cmrivers/ncov/blob/master/COVID-19.pdf
https://www.washingtonpost.com/outlook/coronavirus-pandemic-immunity-vaccine/2020/03/12/bbf10996-6485-11ea-acca-80c22bbee96f_story.html