Medved, you say exactly what I wanted to say. The Russian phonetic system is very different from the English one. Even the sounds B and V are pronounced differently. In Russian they are always voiced before the vowels whether in English they can be partly unvoiced. Also there is such a thing in English as the fortis and lenis contrast in the pairs of voiced - unvoiced consonants which doesn't exist in Russian.
Every sound in a language doesn't exist by itself, on contrary it's an integral part of the phonetic system. So, if you are experiencing a problem with one sound it may indicate your whole system is wrong.
And I agree about the difference in tongue positions in the two languages. I also used to experience that painful feeling in the tongue when I was beginning to speak English. I would say more. When I say some phrase in English which contains a Russian proper name, its easier for me to pronounce that name with English accent than in clear Russian because it takes some time to rearrange my tongue position.
The rule of thumb in mastering Russian phonetics is to pay attention to the place of the tip of your tongue. In Russian it is moved more forward than in English. It almost always touches the backside of the lower or upper front teeth. Try to pronounce the syllables ти-ти-ти, then та-та-та. Then say tee-tee-tee, tah-tah-tah in English. When you say ти-ти-ти, the tip of you tongue MUST be on the backside of your LOWER front teeth and the upper surface of your tongue must touch the teethridge (alveolar ridge) before the air explosion of the "т" sound. And when you pronounce tee-tee-tee in English the tip of the tongue is on the alveolar ridge. When you say та-та-та the tip of the tongue touches the backside of the upper front teeth and the tongue is almost flat. Then, after the explosion it goes to the lower teeth. When you say tah-tah-tah in English the tip of the tongue also touches the alveolar ridge.
So unlike in English, there are not many sounds in Russian which need that the tip of the tongue be placed at the alveolar ridge or near it. They are: the soft "л" [л'], both hard and soft "р" [р, р'], "ж", "ш".