I started taking cephalexin. As I have had mild allergic reaction to penicillin, should I expect serious allergic reactions to this medicatiion?

Mostly not. The incidence of cephalexin allergy in patients with penicillin allergy is in the single digit % and likely not much different from patient without a history of penicillin allergy. However if you had a severe anaphylactic reaction to penicillin, I would suggest an allergy consult just to be safe .