Since we got busy with wedding preparations, my fiancé and I keep fighting. Is this normal?

It is very common, but how the two of you handle this stress is early training for married life. Wedding preparations involve money, two families and deadlines; the stress is real. Set one session a week just for wedding matters, and do not discuss them every time you talk. Divide tasks clearly so no one feels they carry the load alone. When voices start rising, stop and say: ‘Let us continue tomorrow. We are one team.’ Allah praises those “who restrain their anger and pardon people” (Surah Ali 'Imran 3:134). Notice too how your fiancé argues. If the fights come with insults or attempts to control, take it seriously and talk with a counsellor. See communication & emotions.