Hi, A., My little one, who is now 4, had a lot of allergies as a baby, and I am also a nursing instructor. That said, first off I would encourage you to take your baby in to get seen, as 11 weeks is still awfully little. Babies immune systems are not fully-developed until about one year old, so their signs of infection may be much more subtle than an older child's. But, if he is eating well, sleeping ok, peeing and pooping ok, no fever, you are probably ok to wait on the MD appt. You are really limited on meds, so I would try some of the environmental things you can do - like, limit exposure to animals, get rid of carpets/things that hold onto dust/pollen, etc. A big culprit for upper respiratory congestion and skin rashes in babies is food sensitivities. Breastfeeding is best to avoid this. If you are not nursing, but giving "regular" (cow's milk based) formula, you might try a switch to all soy, and try to avoid dairy products. When I did this with my little girl, who was always gunky and coughing and having loose stools, all her symptoms cleared up. She is ok with small amounts of dairy - cheese, yogurt, etc - but they get so much of their nutrition from milk, especially when little, that if that is the problem, a change in milk/formula can bring big results. If it is a food issue, you should see a pretty dramatic change, in maybe 2-3 weeks.
I hope this info might be helpful for you. There may be some health services available to you while in between insurance or with limited insurance. Check with your local health dept. We all pay taxes to support those services, so they will be there when we need them.
Good luck, L.