Hi there kellie118,
You've taken some great steps so far with your iPhone 6 Plus. Do you notice slow performance anywhere else on your iPhone 6 Plus? If it only happens with the Messages app, does this only appear to happen with one conversation thread or multiple conversation threads? Your answers can help determine possible next steps for your iPhone.
Also, the steps and information below might be helpful if you notice this might be happening in multiple apps or with multiple features:
Keep your device from getting too hot or cold
iOS or iPadOS adjusts your device's performance if it's become too warm due to external conditions, like being left in a hot car or used for an extended time in direct sunlight. Move your device to a cooler location and let its temperature adjust.
Very cold temperatures can also slow your device. If your device runs slowly after being exposed to cold, move it to a warmer location.
Learn more about acceptable operating temperatures >
Look at your battery health
All rechargeable batteries are consumable components that become less effective as they chemically age. Over time, the rechargeable batteries in all iPhone and iPad models will diminish in their capacity and peak performance and will eventually need to be replaced. iOS can show show battery health and recommend if an iPhone battery needs to be replaced. Go to Settings > Battery and tap Battery Health. Battery Health is available only on iPhone.
Check your iPhone battery >
Get more help
* A touch screen that responds to taps incorrectly can make your device seem slow. If you think that your touch screen isn't responding correctly, try restarting your iPhone, iPad, or iPod touch. If that doesn't work, and the issue occurs in the same area of the screen in multiple apps, you might need to contact Apple Support.
That information is from this article: If your iPhone or iPad is running slow
Another step that can help is to ensure your iPhone 6 Plus is fully up-to-date, as that can also help resolve unexpected issues. If needed, this article shows how: Update your iPhone or iPad
Please let us know if those steps help or if you've already tried those steps as well.
Take care.