OP, it sounds like you have more than one thing dragging you down. For straight heartache I'd say try to push through, as it is normal and natural to feel pain over that. But with work and health issues too, this sounds like too much to bear on top.
You could try extreme self care first for a couple of weeks, as physically, that would have the benefit of you not having to endure the unpleasant side effects of ADs.
Extreme self care would involve putting aside at least 2-3 hours a day to look after yourself through journalling, meditation, affirmations, long baths with lovely oils, salts or bubbles, gentle yoga sessions. You would need to arm yourself with all your favourite old sit coms/feel good films, escapist novels, soothing upbeat music etc and lose yourself in them. You would get out in nature every day for at least an hour if possible (can be in 2-3 short bursts if work makes it hard to take a whole hour.) Feed the birds, try to catch sunrise or sunset or the golden hour (late afternoon sun). Spend some time focusing on creating a bucket list. Make it projects that involve you and you alone or you and friends/family, not things you had intended to do with your loved one. Start crossing things off your bucket list - plan things, book things, experiment. You could also try and book some free counselling sessions via NHS self referral or some self help on relationship break ups via books or online resources. Also, look up resources online for Self Compassion which help you be kind to yourself when you feel really low about who you are or how your life is going.
That might sound daunting, but even doing small easy steps towards self care will help, such as eating fresh fruit each day or having coffee in the garden to get some fresh air, or slobbing out in front of Frazier reruns or doing a 5 minute yoga with Adriene stretch online. It's important to to acknowledge that you are bothering to take care of yourself.
I'd chat with your GP and ask for a fast acting AD (so, not Prozac!) such as Citalopram or Sertraline, for a 2-3 month stint to give you breathing space. Expect to feel unpleasant physical side effects at first and watch out - they can leave you absolutely shattered with sleepy exhaustion.
I hope you are able to be kind to yourself and take the steps you need to start feeling better.