Yeah there are lots of ways getting better can make you feel worse for a while, although usually it is temporary. Therapy/counselling bringing up issues to work through is one, often after a therapy session I feel terrible while I'm processing stuff. As you improve you may also find yourself having to face real life situations you used to avoid, so also feeling worse due to that until hopefully you have managed to handle them in some way.

But also meds - not just biological side effects. One of the major issues is anti depressants (and sometimes also antipsychotics) can help a person's motivation and concentration improve but if they were so low or so distracted they couldn't motivate themselves to harm themselves sometimes that can backfire as suddenly they have the means to do it but still are not well enough for the feelings to have fully subsided so are more at risk for a while. It's a well known paradoxical effect to be mindful of.

I would stress this is usually just part of the healing process and eventually things should improve. However if you are having side effects it's important to get those checked out.