Yes, if you are receiving qualifying instruction, you sure want to be logging it in your personal pilot logbook! For a short period, you can recreate entries which have not been made and should have been, by going back the the flying school records, though that is not something which should be expected months or years later. There is not reason to fly as a student receiving training, solo, or PIC, without recording that experience for future qualification. Very certainly your instructor should have provided you with a pilot training record following the first training flight. Follow that up with he/she....