@candiecoatediv How long you have before the game becomes unplayable on your current laptop will depend on your tolerance for lag and low graphics settings; everyone is different. You also might find that if you play a bit on your boyfriend's laptop, it will be harder to go back to yours. I happily played Sims 3 for years on an older MacBook Pro than yours (although it had a dedicated graphics card), but I couldn't deal with that now that I've seen what it's like to have smooth play on ultra settings.
The site I linked is a good place to buy, as long as your computer comes from Newegg itself and not one of the third parties that also sell through the company. (I excluded those options.) Depending on what you're looking for, you might save a lot of money there, although Amazon is usually not too much more expensive.
As to the laptop you linked, it's better in every way than the first one I linked, except for the graphics card. But the card is the single biggest determining factor in how Sims 4 will run on your computer. A 1660 ti is a bit of overkill for TS4, but a 1650 may not be quite enough if your goal is to run all future packs on ultra settings. It will handle ultra settings just fine now; this is more about futureproofing and giving yourself a bit of margin to work with.
If the other specs are what caught your attention, you may be better off getting this $1,200 laptop from CyberpowerPC with the same processor and RAM and a 1660 ti, and paying an extra $50 to upgrade the SSD to the 1 TB version.
https://www.cyberpowerpc.com/system/Tracer-III-15V-VR-300
Or, for example, you could get this Acer Predator Helios ($1000) with an Nvidia 1060 6 GB, 16 GB RAM, and last year's version of the same processor. It only has a small 256 GB SSD, but its second hard drive slot is user-accessible, and a 1 TB SSD might cost you $90.
https://www.amazon.com/Acer-Predator-Overclockable-Aeroblade-PH315-51-78NP/dp/B07CTHLX8C
Anyway, there are a lot of good options in your price range, and the best one will depend on what features are most important to you. If and when you're ready to buy, I'd be happy to find you a few models that have what you want.