It is normal to feel a little tight, especially if it is dry.
It doesn't sound like you're washing it often enough. 1x in the shower and one wipe with water is an invitation for infection. You should be washing it with a gentle, unscented, antibacterial soap or a special tattoo soap at LEAST 3 times a day. A woman who has been tattooing 30 years or so recommended Noxzema in the pump bottle and it works amazingly, as strange as it sounds. I've used Noxzema on at least 12 tattoos (and I'm not talking tiny stuff-I'm talking pieces taking between 3-5 hours a piece). I wash my tattoos 3-5 times a day, dry them careful (patting dry) with paper towels, and then apply the ointment like i'm buttering an ant's butt-- meaning, just a tiny, thin layer so you don't heal out any color.
Once it starts peeling, I switch to a mild lotion. I continue to wash it (probably 3 times a day as opposed to more). WHen the peeling is done, you'll still want to be putting lotion on the area as tattooed skin tends to dry out more easily than other skin, and the first few weeks, it will be inclined to be extra dry and a little sensitive.
While healing, keep it very clean, don't touch it with dirty hands, try to keep it out of direct sunlight, DO NOT get it sunburned, do not go swimming for at least 2 weeks, and avoid constricting clothing over it if possible. Get good sleep, eat well, drink lots of water so you speed the healing process by keeping yourself well.
Once it is fully healed, always put sunscreen on the tattoo when it will be exposed to a lot of sun, as you want to maintain the integrity of the lines for as long as possible.
Good luck :)