When I was a teenager I was homeless and sometimes living as male, and even when I was openly female I didn't have appropriate places to deal with this stuff. I really wish I could convince you to keep trying with tampons or cups until they work for you. It's very difficult to manage pads, and the smell can be frustrating even when nobody else notices.
You have to practice and be really okay with and good at whatever method you choose. If you do come around to tampons or a cup, get used to using your finger to rearrange it if it isn't comfortable. Nobody will ask why your hand is in your pants, ever. As long as you don't make eye contact it isn't going to draw attention, and if someone does notice they don't want to talk about it.
With tampons I always had a clean one in a pocket, and a folded piece of paper or a food wrapper in another pocket. You stick your hand in, turn away if you need to root around, pull out the dirty one and enclose it in the paper or plastic, and rip open and insert the clean one. It sounds daunting but it's not difficult. I did this for years without trouble. Most people don't care enough to confront you even if they do believe you are acting strangely.
If you do need to keep using pads, or if you just want more wiggle room in general, I agree with asking for a garbage bin or some other thing that might help. Lots of humans have medical problems that affect how they use the restroom and I doubt HR or whoever you deal with is going to ask a lot of questions.
