I went out last night with a supportive strapless bra under my dress. Before I even got to the restaurant I’d whipped it off in the car as it was so restrictive and uncomfortable!
Lockdown has been so nice, with no need for a bra and comfy elasticated lounging trousers all day. Having to wear real clothes is a right PITA.
If you don’t want to wear one, then don’t. Some people (men) may notice, most probably won’t. Some may comment, so if you’re strong enough to ignore and not feel anxious if someone happens to comment or stare, go for it. It’s absolutely your right to go about your business without having to truss up your boobs to stop people seeing that you have them.
Otherwise as others have suggested, there are more comfy varieties than a standard underwired one.
But the underlying issue is the effect hormonal contraception has on you. If the implant is causing you problems, make sure your GP takes that seriously. Yes we’re all very lucky that we can be in control of our own fertility these days bla bla bla but can’t you imagine men putting up with the myriad of side effects caused by the pill/implants etc?
Anyway, welcome to Mumsnet, it can be a place of great support, but it has also been infiltrated by trolls and people are rightly wary of giving away personal information to perverts and trouble makers, which can be used against us with screenshots and malicious reports etc, which is why your initial post was greeted with such suspicion.
As a handy pointer, on MN most posters don’t use their real name, we don’t use emojis (except the official pixelated MN emojis) , LoLs or kisses. We are generally straight talking, direct (bordering on rude!) and sweary - which is part of what makes the site unique. It also takes a bit of getting used to if you’re generally of a sunny disposition and like to end your messages with smiley faces and kisses 
You need a thick skin and a sense of humour to feel at home here, but if you read more than you post, you’ll get a good idea of the general tone of the place and hopefully find some support for parenting issues as well as style and beauty ones.