Struggling with university

Is there a reason you're not receiving DSA if you have a disability? It's good that your uni has offered some alternative help. I appreciate it's hard to know in advance what might help or not, but I'd say it's probably worth trying the help that they're offering. If you find it unhelpful, or triggering - or if it ends up not being the right time to try it - you can always stop it
Really sorry to hear about the distressing thoughts, that can feel overwhelming and all-encompassing. And can be hard to manage Have you confided in anyone at your uni that you're having these thoughts? Or any family and friends? Please don't suffer alone in silence. If it's hard to tell someone you know/someone at your uni, perhaps you could try talking to a helpline like The Samaritans? Or Shout?

I felt like my disability wasn't severe enough to justify DSA and I also forgot about it until I tried to get support. I do talk to my family about my issues (not the thoughts though), but they don't seem that interested. I did mention it as part of the form to fill out for support. Since the support assessment, I haven't heard back from the support team. It might because they have a sort of waiting list.

I'm sorry your family don't seem interested Have you since changed your mind about DSA? If not, I'd urge you to reconsider and try and apply asap (if you have the energy/spoons to. I appreciate filling in forms can take up a lot of headspace and cause anxiety, but it'll really be worth it if you get it).
How long ago was your support assessment? There probably is a waiting list, and also there might be a triage aspect to it, where they're working out what support would be best and which dept. should provide that.
Please do keep an eye on the distressing thoughts. A problem shared is not always a problem halved, I do acknowledge that. I just worry if you keep these thoughts to yourself, they will magnify and perhaps even increase in severity and frequency.
Here's some webpages for you, about the helplines I mention:
Contacting The Samaritans
About Shout text support
Also if you're aged under 35, you might consider looking at Papyrus
Take care and please don't hesitate to reach out (and advocate) for the help you need and deserve. A disability is a disability, and it sounds like you're also struggling with your mental health. It's not about whose or which disability is worse