Question: By Jiu Jitsu are you referring to BJJ (chiefly groundwork focused) or to something more akin to Japanese Jiu Jitsu (more standup focused)?

Outside of that, I would rank your options as follows (1 being most relevant to your situation):

1.) Judo

2.) Boxing

3.) Jiu Jitsu (Assuming BJJ)

4.) Karate or Muay Thai

Reasoning:

1.) I rank Judo as the first choice for your situation because it will most quickly help you become accustomed to being uncomfortably close with your opponent/assailant/whoever. (One of the maxims for more traditional kodokan Judo is that most of the techniques should/can be performed within the space allocated by a phone booth.) BJJ will also help in this respect (if not more) but Judo has the added benefit of throws (aka, how to hit people with the earth). While every martial art has some bare minimum for upper body strength, throws lend themselves to weaker individuals with good technique and timing. Judo also has groundwork techniques. Though they are much simpler (imo) and not as refined as BJJ groundwork, that relative simplicity makes it a better introduction point to how to fight on the ground (imo). Keep in mind however, it will take time and dedicated practice to be able to execute throws