First, I'm so sorry about your previous relationship, OP.
Second, my experience with dating (at age 22 in a liberal city so it might be different for you) has been that even if you're not super keen on the idea of dating multiple people, other people likely will be, so if you happen to get attached, they might still not feel the same. If you decide, you're ok with that, I'd stick to dating one person at a time. Otherwise, I've found it has helped me not get attached when I 'date' multiple people at once. It does get tiring though, so as I'm now working, if I ever do go on dates I usually do one a week, so in essence I'm 'dating' one person at a time.
Does that make sense? Lmk if you have any questions! Cheers :)