Hi @lippyqueen I'm a nail tech and 'usually' a vertical split is from damage at some point and can be very hard to grow out. I have had clients with this on various nails and they either have a gel polish manicure which will strengthen the nail and help it grow out or some ladies will just have a clear base and top coat in gel so they don't have to worry about coming in to get colour changed after three weeks and let it grow out naturally.
If you don't want to go down the visiting a salon route there's a few things you can do. Use a small piece of a tea bag cut to cover the front half of your nail, (make sure it covers at least 2mm above the split) put nail glue on your nail, stick the tea bag fabric and let it dry completely. Repeat this step again and then using a fine nail file smooth the top and the front edges. Cover then with a clear top coat.
Sally Hansen do some good products for strengthening and repair aswell as a good top coat.
The reason it takes forever for vertical split nails to heal is because the actual split usually goes further up into the nail bed so you think you've got it filed out, but the damage goes further up.
If you were coming to me I'd be expecting it to take 6 weeks (2 manicures) to say it's been safely grown out so you might decide to do that as the gel polish will protect your nail and give it strength to prevent any further damage.
If you do go for the manicure ALWAYS have your nail technician remove the gel polish as trying to remove or pick it off yourself will cause damage to your natural nails.
If you want to ask me anything, please do and good luck xx