Hi OP, I'm sorry about your mum - I'm going through the process of getting my dad into a nursing home at the moment so I know what you mean about stress - it's easy to overlook self care during stuff like that.
Regarding your skin, there are a few good ingredients that can help improve skin tone and texture.
The first one is Vitamin C serum. This is an antioxidant that can help to brighten and even out skin tone. I use one from a brand called Geek and Gorgeous called C-Glow, (which is a great brand as not expensive, but you can't get it in shops only online) - but there are lots of brands that do them. Look for 'L-ascorbic acid' as the main ingredient, as it has the best researched one. If you have very sensitive skin you may not tolerate it well, but if you have normal to dry skin you should be ok.
The second one would be a retinol product. This works to increase cellular turnover and increase collagen production over time (basically makes your skin act like younger skin). There are loads of retinol products you can get over the counter in different formulas and price points. Pick one that suits your skin type and budget and use it at nighttime after cleansing.
If you want, you could try going down the route of prescription strength retinol (called tretinoin), which can be gotten from subscription services like Skin & Me or Dermatica, or from a dermatologist but that's expensive.
However, I always advise caution with tretinoin as it can take a few months to see results and the irritation and peeling you get from it can be very off-putting, whereas the over the counter retinols are much weaker and therefore less irritating.
The last thing I would recommend would be a chemical exfoliant, like glycolic acid or salicylic acid (glycolic acid is better for normal to dry skin whereas salicylic acid works better on oily skin). Just be careful not to overuse them because they can dry out the skin, especially if you are using other 'active' ingredients like vitamin c or retinol. I only use glycolic acid about once a week or even less.
Also (sorry for the essay), if you are going to start using any of these I would recommend you use a high strength SPF everyday, as they will make your skin more sensitive to sun damage. And maybe try and introduce one ingredient at a time for a few weeks to see how well your skin tolerates them.