That is correct. You may need reading glasses or have to do monovision where your non dominant eye is undercorrected for near vision
That is quite a jump in prescription, how quickly did your vision change that much? Before the new prescription, didn't you have trouble functioning with essentially -5D of myopia, putting your best focal point at 20 cm = 7.87 inches? I'm guessing you didn't need to drive? I'm just wondering if the change was sudden, if it might indicate other eye issues which might go along with the problem with seeing near while wearing distance correction.
As people age they gradually lose the ability for their eye to change focus from far to near, the number of diopters the eye can change focus goes down over time. When people corrected for good distance vision start to experience problems seeing near well enough without additional correction, its called presbyopia, its why often you'll see older people needing reading glasses and why they sell readers over the counter in many stores.
However usually in the US (I don't know what country you are in), presbyopia issues aren't usually evident until the early-mid forties, though a quick check shows in some countries, the age is a bit lower, but for most modern countries (I don't know where you are) you seem young to have this issue (though some do). Your description suggests you may have "premature presbyopia" or "early onset presbyopia", which has a number of causes they can consider. Oddly I see hyperopia suggested as a potential risk factor, but not high myopia, though some suggest those doing more near work may be at risk, it isn't clear from a quick skim if that is the case.
Most high myopes do find vision better with contacts, with the added advantage with presbyopia that you can have a pair of reading glasses you put over them for near. If you have two distances you wish to see like a computer and reading closer in, some use bifocals, trifocals, or progressive glasses (called varifocals in some countries), which are sometimes described as "no-line-bifocals" but they may provide a continuous range of vision rather than just 2 focal points.
If you don't use your distance vision much, you could also leave yourself undercorrected with contacts to see better at intermediate or near, and then wear glasses over your contacts for distance vision.
In my case I preferred wearing multifocal contacts, which let you see distance as well as near without needing to look in a different direction like with glasses, and without the need to put on readers. There are tradeoffs, like reduced vision in dim light, but I didn't mind that. Some may see their distance vision not be quite as crisp with a multifocal, though if you managed without good distance correction for a while I'm suspecting that isn't a big concern. Others use "monovision", one eye focused in near to be able to read, which however reduces depth perception since you are using one eye more than another, though most people adapt to it well and don't notice. I preferred multifocals, and figured full depth perception is safer in many contexts than monovision (e.g. pilots aren't allowed to fly with monovision correction in the US, and studies show an increased risk of falls in the elderly with monovision).