Hi Jess. I really hear you. I am doing my PhD and my husband is finishing his undergrad and we have a 16 month old who we share care. We had him in daycare one day a week which he really enjoyed but pulled him out because when we had to move and his new one hasn't worked out. It isn't for everyone but our DS really loves it (or did when we had a great one) and even just one day helps to stay ahead. He gets exposed to lots of things that we don't really do at home. We started about 6 months though.
You also have to find something that is just yours. I am going to start painting because sometimes I am just mentally exhausted and I need something creative to absorb myself in. Exercise and proper nutrition is also really important for keeping up with the day to day - but is often the first thing to go unfortunately.
I can definitely say it gets a lot easier with time. As they get older it gets easier to go out, go to playgroups etc. Plus the whole adjustment to parenthood takes time in itself.
Make sure you get enough sleep and take time when you can to do something you enjoy. And keep an eye on how you are feeling as you may benefit from seeing a counselor or similar. I think many of us struggle with loss of self after having a child.
Big hugs. I hope this helps.