Spells known vs Spells prepared
You may be confusing the concepts of spells known and prepared.
Bards have a number spells known. From the Spellcasting section for Bards:
The Bard table shows how many spell slots you have to cast your bard spells of 1st level and higher.
Spells Known of 1st Level and Higher
You know four 1st-level spells of your choice from the bard spell list.
The Spells Known column of the Bard table shows when you learn more bard spells of your choice.
This means that any spell you know as a Bard is always available to cast.
The wizard has both a spellbook and a number of spells prepared:
At 1st level, you have a spellbook containing six 1st-level wizard spells of your choice. Your spellbook is the repository of the wizard spells you know, except your cantrips, which are fixed in your mind.
Preparing and Casting Spells
The Wizard table shows how many spell slots you have to cast your wizard spells of 1st level and higher. (...)
You prepare the list of wizard spells that are available for you to cast. To do so, choose a number of wizard spells from your spellbook equal to your Intelligence modifier + your wizard level (minimum of one spell).
This means wizards store all their spells (other than cantrips) in a spellbook, then choose a number of them each day to have prepared, which are the spells that will be available to cast using spell slots for that day. There are methods to copy spells into a wizard's spellbook which means that they can have a nearly unlimited number of spells known but they can still only prepare a few of them each day.
In your case, the spells that you have available to cast are all spells known as a Bard plus any spell prepared as a Wizard, in which case the total number of spells available is indeed 11 Bard spells plus 5 Wizard spells but you actually know 11 Bard spells and 6 wizard spells (or more if you add some to the spellbook)
The high number of available spells is not an issue
Yes you will have a total of 16 spells available to cast, which may seem a lot for a 7th level character, but this is merely a side effect of multiclassing.
When multiclassing spellcasting classes you tend to get a lot of different spells with the downside that you get less higher level spells (remember that the maximum level for spells learned depends on individual class levels), regardless of available spell slots.
For example: with your charisma of 19 and Intelligence of 19, you could also have these levels at total character level 7:
- Bard 2 (4 spells),
- Sorcerer 1 (2 spells),
- Warlock 1 (2 spells),
- Paladin 2 (5 spells prepared),
- Wizard 1 (5 spells prepared)
For a total of 18 available spells! If you have the stats to also multiclass into cleric or druid you could even increase this number further. But do note that in my example all of these spells are lvl 1 spells which may not be ideal.