According to Sage Advice
Is there a limit on the number of spells you can cast on your turn?
There’s no rule that says you can cast only X number of spells on your turn, but there are some practical limits. The main limiting factor is your action. Most spells require an action to cast, and unless you use a feature like the fighter’s
Action Surge, you have only one action on your turn.
If you cast a spell, such as
healing word, with a bonus action, you can cast another spell with your action, but that other spell must be a cantrip. Keep in mind that this particular limit is specific to spells that use a bonus action. For instance, if you cast a second spell using
Action Surge, you aren’t limited to casting a cantrip with it.
In addition, we've always ruled that you can cast a reaction spell on your turn. It's explicitly spelled out that you can take a reaction on your turn. It's not really a big issue from a balance perspective because you don't get another reaction until your next turn anyway. Also Sage Advice
Can you cast a reaction spell on your turn?