I see you've started training to improve your abilities and that's good, so continue with that. As you won't be able to train to improve your constitution I advise using the points you get when you gain a level to improve this to the maximum of 200 points, and in the meantime train to develop your other abilities. Using the training facilities in safe houses to increase the limit of these will help you (those marked 100% safe have fully upgraded training facilities and are ideal for allowing you to realise your full fighting potential, so if you're near one use that).
If you don't yet have a sidearm, get one for close combat. You may salvage one from a fight, but gun shops (e.g. the Hardballer Gun store at 41,28) also stock them so if you can buy the best one you can afford and ammo as well. Going on missions will help to earn you money to do this and buy ammo, as well as gaining experience and food. You can salvage this also for free but don't rely on this alone. Buy or salvage a bladed or bludgeoning weapon for close combat if you can. This needs no ammo and will benefit from your improved close combat and strength abilities when in use.
Until you feel confident enough of your abilities, your armour (a helmet would also help) and weapons try to keep within the down-town area as encounters with walkers, animals or raiders will have relatively low numbers. Crafting, salvaging or buying a bag to improve your carrying capacity will also help. Gathering building materials and items to fit out safe houses will gain you experience when applied or recycled in a house.
And don't forget to get to a safe location before logging off or your SP runs out. Sleeping rough with walkers and wild animals loose will put you in danger. Good luck and have fun!
